Special identities for Bol algebras

Bol algebras appear as the tangent algebra of Bol loops. A (left) Bol algebra is a vector space equipped with a binary operation [a, b] and a ternary operation {a, b, c} that satisfy five defining identities. If A is a left or right alternative algebra then A(b) is a Bol algebra, where [a, b] := ab - ba is the commutator and {a, b, c} := < b, c, a > is the Jordan associator. A special identity is an identity satisfied by Ab for all right alternative algebras A, but not satisfied by the free Bol algebra. We show that there are no special identities of degree <= 7, but there are special identities of degree 8. We obtain all the special identities of degree 8 in partition six-two. (C) 2011 Elsevier Inc. All rights reserved.

On simple Lie algebras over a field of characteristic 2

We prove that the simple Lie algebras constructed by G. Jurman (2004) in 121 are isomorphic to Hamiltonian algebras. As a corollary we answer all questions formulated in G. Jurman (2004) [2] about isomorphisms of these algebras. (C) 2012 Elsevier Inc. All rights reserved.

Multiparameter twisted Weyl algebras

We introduce a new family of twisted generalized Weyl algebras, called multiparameter twisted Weyl algebras, for which we parametrize all simple quotients of a certain kind. Both Jordan's simple localization of the multiparameter quantized Weyl algebra and Hayashi's q-analog of the Weyl algebra are special cases of this construction. We classify all simple weight modules over any multiparameter twisted Weyl algebra. Extending results by Benkart and Ondrus, we also describe all Whittaker pairs up to isomorphism over a class of twisted generalized Weyl algebras which includes the multiparameter twisted Weyl algebras. (C) 2011 Elsevier Inc. All rights reserved.

Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields

We prove that any two Poisson dependent elements in a free Poisson algebra and a free Poisson field of characteristic zero are algebraically dependent, thus answering positively a question from Makar-Limanov and Umirbaev (2007) [8]. We apply this result to give a new proof of the tameness of automorphisms for free Poisson algebras of rank two (see Makar-Limanov and Umirbaev (2011) [9], Makar-Limanov et al. (2009) [10]). (C) 2011 Elsevier Inc. All rights reserved.

Algebras determined by their supports

In this paper, we introduce and study a class of algebras which we call ada algebras. An artin algebra is ada if every indecomposable projective and every indecomposable injective module lies in the union of the left and the right parts of the module category. We describe the Auslander-Reiten components of an ada algebra which is not quasi-tilted, showing in particular that its representation theory is entirely contained in that of its left and right supports, which are both tilted algebras. Also, we prove that an ada algebra over an algebraically closed field is simply connected if and only if its first Hochschild cohomology group vanishes. (C) 2011 Elsevier B.V. All rights reserved.

Rappresentazioni lineari di SL3(C)

Espongo i fatti di base della teoria delle rappresentazioni con lo scopo di indagare i possibili modi in cui un dato gruppo di Lie o algebra di Lie agisce su uno spazio vettoriale di dimensione finita. Tali risultati verranno applicati all'algebra di Lie del gruppo speciale lineare.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

Pervasive Algebras and Maximal Subalgebras.

A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X) . It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain of pervasive subalgebras on X . (2) It is possible to find a compact Hausdorff space X such that there is an isomorphic copy of the lattice of all subsets of N in the family of pervasive subalgebras of C(X). (3) In the other direction, if A is strongly logmodular, proper and pervasive, then it is maximal. (4) This fails if the word “strongly” is removed. We discuss examples involving Dirichlet algebras, A(U) algebras, Douglas algebras, and subalgebras of H∞(D), and develop new results that relate pervasiveness, maximality, and relative maximality to support sets of representing measures.

Protein kinase C alpha-dependent phosphorylation of the mRNA-stabilizing factor HuR: implications for posttranscriptional regulation of cyclooxygenase-2

In this study, we investigated the molecular mechanisms underlying the ATP analogue adenosine-5'-O-(3-thio)triphosphate-induced nucleocytoplasmic shuttling of the mRNA stabilizing factor HuR in human (h) mesangial cells (MC). Using synthetic protein kinase C (PKC) inhibitors and small interfering RNA approaches, we demonstrated that knockdown of PKC alpha efficiently blocked the ATP-dependent nuclear HuR export to the cytoplasm. The functional importance of PKC alpha in HuR shuttling is highlighted by the high cytosolic HuR content detected in hMC stably overexpressing PKC alpha compared with mock-transfected cells. The ATP-induced recruitment of HuR to the cytoplasm is preceded by a direct interaction of PKC alpha with nuclear HuR and accompanied by increased Ser phosphorylation as demonstrated by coimmunoprecipitation experiments. Mapping of putative PKC target sites identified serines 158 and 221 as being indispensable for HuR phosphorylation by PKC alpha. RNA pull-down assay and RNA electrophoretic mobility shift assay demonstrated that the HuR shuttling by ATP is accompanied by an increased HuR binding to cyclooxygenase (COX)-2 mRNA. Physiologically, the ATP-dependent increase in RNA binding is linked with an augmentation in COX-2 mRNA stability and subsequent increase in prostaglandin E(2) synthesis. Regulation of HuR via PKC alpha-dependent phosphorylation emphasizes the importance of posttranslational modification for stimulus-dependent HuR shuttling.

The Protein-tyrosine-phosphatase SHP2 is phosphorylated on serine residues 576 and 591 by protein kinase C isoforms alpha, beta 1, beta 2, and eta

To study whether protein kinase C (PKC) isoforms can interact with protein-tyrosine-phosphatases (PTPs) which are connected to the insulin signaling pathway, we co-overexpressed PKC isoforms together with insulin receptor, docking proteins, and the PTPs SHP1 and SHP2 in human embryonic kidney (HEK) 293 cells. After phorbol ester induced activation of PKC isoforms alpha, beta 1, beta 2, and eta, we could show a defined gel mobility shift of SHP2, indicating phosphorylation on serine/threonine residues. This phosphorylation was not dependent on insulin receptor or insulin receptor substrate-1 (IRS-1) overexpression and did not occur for the closely related phosphatase SHP1. Furthermore, PKC phosphorylation of SHP2 was completely blocked by the PKC inhibitor bisindolylmaleimide and was not detectable when SHP2 was co-overexpressed with kinase negative mutants of PKC beta 1 and -beta 2. The phosphorylation also occurred on endogenous SHP2 in Chinese hamster ovary (CHO) cells stably overexpressing PKC beta 2. Using point mutants of SHP2, we identified serine residues 576 and 591 as phosphorylation sites for PKC. However, no change of phosphatase activity by TPA treatment was detected in an in vitro assay. In summary, SHP2 is phosphorylated on serine residues 576 and 591 by PKC isoforms alpha, beta 1, beta 2, and eta.

Role and regulation of c-KIT gene expression in tumor growth and metastasis of human melanoma

The purpose of this study was to investigate the role of the c-KIT receptor in the progression of human melanoma and the mechanism(s) for the regulation of c-KIT gene expression in human melanoma.^ The molecular changes associated with the transition of melanoma cells from radial growth phase (RGP) to vertical growth phase (VGP) (metastatic phenotype) are not well-defined. Expression of the tyrosine-kinase receptor c-KIT progressively decreases during local tumor growth and invasion of human melanomas. To provide direct evidence that the metastasis of human melanoma is associated with the loss of c-KIT expression, highly metastatic A375SM cells, which express very low or undetectable levels of c-KIT, were tranduced with the human c-KIT gene. We demonstrated that enforced c-KIT expression in highly metastatic human melanoma cells significantly suppressed their tumorigenicity and metastatic propensity in nude mice. In addition, we showed that the ligand for c-KIT, SCF, induces apoptosis in human melanoma cells expressing c-KIT under both in vitro and in vivo conditions. These results suggest that loss of c-KIT receptor may allow malignant melanoma cells to escape SCF/c-KIT-mediated apoptosis, thus contributing to tumor growth and eventually metastasis.^ Furthermore, we investigated the possible mechanism(s) for the down-regulation of c-KIT gene expression in malignant melanoma. Sequence analysis of the c-KIT promoter indicated that this promoter contains several consensus binding-site sequences including three putative AP2 and two Myb sites. Although Myb was shown to be associated with c-KIT expression in human hemotopoietic cells, we found no correlation between c-KIT expression and Myb expression in human melanoma cell lines. In contrast, we showed that c-KIT expression directly correlates with expression of AP2 in human melanoma cells. We found that highly metastatic cells do not express the transcription factor AP2. Expression of AP2 in A375SM cells (c-KIT-negative and AP2-negative) was enough to restore luciferase activity driven by the c-KIT promoter in a dose-dependent manner. On the other hand, co-expression of the dominant-negative form of AP2 (AP2B) in Mel-501 cells (c-KIT-positive and AP2-positive) resulted in two-fold reduction in luciferase activity. Electrophoretic mobility shift assays revealed that the c-KIT promoter contains functional AP2 binding sites which could associate with AP2 protein. Endogenous c-KIT gene expression levels were elevated in AP2 stably-transfected human melanoma A375SM cells. Expression of exogenous AP2 in A375SM cells inhibited their tumorigenicity and metastatic potential in nude mice. The c-KIT ligand, SCF, also induced apoptosis in the AP2 stably-transfected A375SM cells. The identification of AP2 as an important regulator for c-KIT expression suggests that AP2 may have tumor growth and metastasis inhibitory properties, possibly mediated through c-KIT/SCF effects on apoptosis of human melanoma cells. Since AP2 binding sites were found in the promoters of other genes involved in the progression of human melanoma, such as MMP2 (72 kDa collagenase), MCAM/MUC18 and P21/WAF-1, our findings suggest that loss of AP2 expression might be a crucial event in the development of malignant melanoma. ^

Substantial narrowing of the Niemann–Pick C candidate interval by yeast artificial chromosome complementation

Niemann–Pick disease type C (NP-C) is an autosomal recessive lipidosis linked to chromosome 18q11–12, characterized by lysosomal accumulation of unesterified cholesterol and delayed induction of cholesterol-mediated homeostatic responses. This cellular phenotype is identifiable cytologically by filipin staining and biochemically by measurement of low-density lipoprotein-derived cholesterol esterification. The mutant Chinese hamster ovary cell line (CT60), which displays the NP-C cellular phenotype, was used as the recipient for a complementation assay after somatic cell fusions with normal and NP-C murine cells suggested that this Chinese hamster ovary cell line carries an alteration(s) in the hamster homolog(s) of NP-C. To narrow rapidly the candidate interval for NP-C, three overlapping yeast artificial chromosomes (YACs) spanning the 1 centimorgan human NP-C interval were introduced stably into CT60 cells and analyzed for correction of the cellular phenotype. Only YAC 911D5 complemented the NP-C phenotype, as evidenced by cytological and biochemical analyses, whereas no complementation was obtained from the other two YACs within the interval or from a YAC derived from chromosome 7. Fluorescent in situ hybridization indicated that YAC 911D5 was integrated at a single site per CT60 genome. These data substantially narrow the NP-C critical interval and should greatly simplify the identification of the gene responsible in mouse and man. This is the first demonstration of YAC complementation as a valuable adjunct strategy for positional cloning of a human gene.

A dileucine motif in the C terminus of the β2-adrenergic receptor is involved in receptor internalization

The cytoplasmic C terminus of the β2-adrenergic receptor and many other G protein-coupled receptors contains a dileucine sequence that has been implicated in endosome/lysosome targeting of diverse proteins. In the present study, we provide evidence for an essential role of this motif in the agonist-induced internalization of the β2-adrenergic receptor. Mutation of Leu-339 and/or Leu-340 to Ala caused little changes in surface expression, ligand binding, G protein coupling, and signaling to adenylyl cyclase, when these receptors were transiently or stably expressed in CHO or HEK-293 cells. However, agonist-induced receptor internalization was markedly impaired in the L339,340A double mutant and reduced in the two single mutants. This impairment in receptor internalization was seen by using various approaches to determine internalization: binding of hydrophobic vs. hydrophilic ligands, loss of surface β2-adrenergic receptor immunoreactivity, and immunofluorescence microscopy. The selective effects of these mutations suggest that the C-terminal dileucine motif is involved in agonist-induced internalization of the β2-adrenergic receptor.

Chemotaxis in a lymphocyte cell line transfected with C-C chemokine receptor 2B: Evidence that directed migration is mediated by βγ dimers released by activation of Gαi-coupled receptors

Chemotaxis is mediated by activation of seven-transmembrane domain, G protein-coupled receptors, but the signal transduction pathways leading to chemotaxis are poorly understood. To identify G proteins that signal the directed migration of cells, we stably transfected a lymphocyte cell line (300-19) with G protein-coupled receptors that couple exclusively to Gαq (the m3 muscarinic receptor), Gαi (the κ-opioid receptor), and Gαs (the β-adrenergic receptor), as well as the human thrombin receptor (PAR-1) and the C-C chemokine receptor 2B. Cells expressing receptors that coupled to Gαi, but not to Gαq or Gαs, migrated in response to a concentration gradient of the appropriate agonist. Overexpression of Gα transducin, which binds to and inactivates free Gβγ dimers, completely blocked chemotaxis although having little or no effect on intracellular calcium mobilization or other measures of cell signaling. The identification of Gβγ dimers as a crucial intermediate in the chemotaxis signaling pathway provides further evidence that chemotaxis of mammalian cells has important similarities to polarized responses in yeast. We conclude that chemotaxis is dependent on activation of Gαi and the release of Gβγ dimers, and that Gαi-coupled receptors not traditionally associated with chemotaxis can mediate directed migration when they are expressed in hematopoietic cells.

Identification of eIF2Bγ and eIF2γ as cofactors of hepatitis C virus internal ribosome entry site-mediated translation using a functional genomics approach

The 5′-untranslated region of hepatitis C virus (HCV) is highly conserved, folds into a complex secondary structure, and functions as an internal ribosome entry site (IRES) to initiate translation of HCV proteins. We have developed a selection system based on a randomized hairpin ribozyme gene library to identify cellular factors involved in HCV IRES function. A retroviral vector ribozyme library with randomized target recognition sequences was introduced into HeLa cells, stably expressing a bicistronic construct encoding the hygromycin B phosphotransferase gene and the herpes simplex virus thymidine kinase gene (HSV-tk). Translation of the HSV-tk gene was mediated by the HCV IRES. Cells expressing ribozymes that inhibit HCV IRES-mediated translation of HSV-tk were selected via their resistance to both ganciclovir and hygromycin B. Two ribozymes reproducibly conferred the ganciclovir-resistant phenotype and were shown to inhibit IRES-mediated translation of HCV core protein but did not inhibit cap-dependent protein translation or cell growth. The functional targets of these ribozymes were identified as the gamma subunits of human eukaryotic initiation factors 2B (eIF2Bγ) and 2 (eIF2γ), respectively. The involvement of eIF2Bγ and eIF2γ in HCV IRES-mediated translation was further validated by ribozymes directed against additional sites within the mRNAs of these genes. In addition to leading to the identification of cellular IRES cofactors, ribozymes obtained from this cellular selection system could be directly used to specifically inhibit HCV viral translation, thereby facilitating the development of new antiviral strategies for HCV infection.