Hyperbolic unit groups and quaternion algebras

We classify the quadratic extensions K = Q[root d] and the finite groups G for which the group ring o(K)[G] of G over the ring o(K) of integers of K has the property that the group U(1)(o(K)[G]) of units of augmentation 1 is hyperbolic. We also construct units in the Z-order H(o(K)) of the quaternion algebra H(K) = (-1, -1/K), when it is a division algebra.

Hyperbolicity of semigroup algebras

Let A be a finite-dimensional Q-algebra and Gamma subset of A a Z-order. We classify those A with the property that Z(2) negated right arrow U(Gamma) and refer to this as the hyperbolic property. We apply this in case A = K S is a semigroup algebra, with K = Q or K = Q(root-d). A complete classification is given when KS is semi-simple and also when S is a non-semi-simple semigroup. (c) 2008 Elsevier Inc. All rights reserved.

Tilt-critical algebras of tame type

Let A be a finite dimensional k-algebra over an algebraically closed field. Assume A=kQ/I where Q is a quiver without oriented cycles. We say that A is tilt-critical if it is not tilted but every proper convex subcategory of A is tilted. We describe the tilt-critical algebras which are strongly simply connected and tame.

Structural and Biochemical Characterization of Peroxiredoxin Q beta from Xylella fastidiosa CATALYTIC MECHANISM AND HIGH REACTIVITY

The phytopathogenic bacterium Xylella fastidiosa is the etiological agent of various plant diseases. To survive under oxidative stress imposed by the host, microorganisms express antioxidant proteins, including cysteine-based peroxidases named peroxiredoxins. This work is a comprehensive analysis of the catalysis performed by PrxQ from X. fastidiosa (XfPrxQ) that belongs to a peroxiredoxin class still poorly characterized and previously considered as moderately reactive toward hydroperoxides. Contrary to these assumptions, our competitive kinetics studies have shown that the second-order rate constants of the peroxidase reactions of XfPrxQ with hydrogen peroxide and peroxynitrite are in the order of 107 and 106 M(-1) s(-1), respectively, which are as fast as the most efficient peroxidases. The XfPrxQ disulfides were only slightly reducible by dithiothreitol; therefore, the identification of a thioredoxin system as the probable biological reductant of XfPrxQ was a relevant finding. We also showed by site-specific mutagenesis and mass spectrometry that an intramolecular disulfide bond between Cys-47 and Cys-83 is generated during the catalytic cycle. Furthermore, we elucidated the crystal structure of XfPrxQ C47S in which Ser-47 and Cys-83 lie similar to 12.3 angstrom apart. Therefore, significant conformational changes are required for disulfide bond formation. In fact, circular dichroism data indicated that there was a significant redox-dependent unfolding of alpha-helices, which is probably triggered by the peroxidatic cysteine oxidation. Finally, we proposed a model that takes data from this work as well data as from the literature into account.

ADCK3, an ancestral kinase, is mutated in a form of recessive ataxia associated with coenzyme Q(10) deficiency

Muscle coenzyme Q(10) (CoQ(10) or ubiquinone) deficiency has been identified in more than 20 patients with presumed autosomal-recessive ataxia. However, mutations in genes required for CoQ(10) biosynthetic pathway have been identified only in patients with infantile-onset multisystemic diseases or isolated nephropathy. Our SNP-based genome-wide scan in a large consanguineous family revealed a locus for autosomal-recessive ataxia at chromosome 1q41. The causative mutation is a homozygous splice-site mutation in the aarF-domain-containing kinase 3 gene (ADCK3). Five additional mutations in ADCK3 were found in three patients with sporadic ataxia, including one known to have CoQ(10) deficiency in muscle. All of the patients have childhood-onset cerebellar ataxia with slow progression, and three of six have mildly elevated lactate levels. ADCK3 is a mitochondrial protein homologous to the yeast COQ8 and the bacterial UbiB proteins, which are required for CoQ biosynthesis. Three out of four patients tested showed a low endogenous pool of CoQ(10) in their fibroblasts or lymphoblasts, and two out of three patients showed impaired ubiquinone synthesis, strongly suggesting that ADCK3 is also involved in CoQ(10) biosynthesis. The deleterious nature of the three identified missense changes was confirmed by the introduction of them at the corresponding positions of the yeast COQ8 gene. Finally, a phylogenetic analysis shows that ADCK3 belongs to the family of atypical kinases, which includes phosphomositide and choline kinases, suggesting that ADCK3 plays an indirect regulatory role in ubiquinone biosynthesis possibly as part of a feedback loop that regulates ATP production.

Indecomposable and noncrossed product division algebras over function fields of smooth p-adic curves

We construct indecomposable and noncrossed product division algebras over function fields of connected smooth curves X over Z(p). This is done by defining an index preserving morphism s: Br(<(K(X))over cap>)` --> Br(K(X))` which splits res : Br(K (X)) --> Br(<(K(X))over cap>), where <(K(X))over cap> is the completion of K (X) at the special fiber, and using it to lift indecomposable and noncrossed product division algebras over <(K(X))over cap>. (C) 2010 Elsevier Inc. All rights reserved.

Identification of geodesic chirping Alfven modes and q-factor estimation in hot core tokamak plasmas in ASDEX Upgrade

Alfven eigenmodes (AE) driven by ion cyclotron resonance heating are usually registered by different diagnostic channels in the hot core plasmas of large tokamaks like JET and ASDEX Upgrade. These AE appear very near to the extremum points of Alfven wave continuum, which is modified by the geodesic effect due to poloidal mode coupling. It is shown that the AE spectrum may be explored as the magnetic spectroscopy (like Alfven cascades by Sharapov et al 2001 Phys. Lett. A 289 127) to determine the q-factor minimum and geodesic frequency at the magnetic axis in standard sawtoothed discharges without reversed shear.

Coherent state quantization of paragrassmann algebras

By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators leads to interesting conclusions.

The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.

On the Derived Categories and Quasitilted Algebras

In this paper, we present some results on the bounded derived category of Artin algebras, and in particular on the indecomposable objects in these categories, using homological properties. Given a complex X*, we consider the set J(X*) = {i is an element of Z vertical bar H(i)(X*) not equal 0} and we define the application l(X*) = maxJ(X*) - minJ(X*) + 1. We give relationships between some homological properties of an algebra and the respective application l. On the other hand, using homological properties again, we determine two subcategories of the bounded derived category of an algebra, which turn out to be the bounded derived categories of quasi-tilted algebras. As a consequence of these results we obtain new characterizations of quasi-tilted and quasi-tilted gentle algebras.

COMMUTATIVE FINITE-DIMENSIONAL ALGEBRAS SATISFYING x(x(xy))=0 ARE NILPOTENT

We investigate the structure of commutative non-associative algebras satisfying the identity x(x(xy)) = 0. Recently, Correa and Hentzel proved that every commutative algebra satisfying above identity over a field of characteristic not equal 2 is solvable. We prove that every commutative finite-dimensional algebra u over a field F of characteristic not equal 2, 3 which satisfies the identity x(x(xy)) = 0 is nilpotent. Furthermore, we obtain new identities and properties for this class of algebras.

Examples of Self-Iterating Lie Algebras, 2

We study properties of self-iterating Lie algebras in positive characteristic. Let R = K[t(i)vertical bar i is an element of N]/(t(i)(p)vertical bar i is an element of N) be the truncated polynomial ring. Let partial derivative(i) = partial derivative/partial derivative t(i), i is an element of N, denote the respective derivations. Consider the operators v(1) = partial derivative(1) + t(0)(partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...))))); v(2) = partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...)))). Let L = Lie(p)(v(1), v(2)) subset of Der R be the restricted Lie algebra generated by these derivations. We establish the following properties of this algebra in case p = 2, 3. a) L has a polynomial growth with Gelfand-Kirillov dimension lnp/ln((1+root 5)/2). b) the associative envelope A = Alg(v(1), v(2)) of L has Gelfand-Kirillov dimension 2 lnp/ln((1+root 5)/2). c) L has a nil-p-mapping. d) L, A and the augmentation ideal of the restricted enveloping algebra u = u(0)(L) are direct sums of two locally nilpotent subalgebras. The question whether u is a nil-algebra remains open. e) the restricted enveloping algebra u(L) is of intermediate growth. These properties resemble those of Grigorchuk and Gupta-Sidki groups.

Crossed products by twisted partial actions and graded algebras

For a twisted partial action e of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A x(Theta) G is proved to be associative. Given a G-graded k-algebra B = circle plus(g is an element of G) B-g with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B-1 x(Theta) G for some twisted partial action of G on B-1. The equality BgBg-1 B-g = B-g (for all g is an element of G) is one of the ingredients of the criteria, and if it holds and, moreover, B has enough local units, then it is shown that B is stably isomorphic to a crossed product by a twisted partial action of G. (c) 2008 Elsevier Inc. All rights reserved.

POLYNOMIAL AND GROUP IDENTITIES IN ALTERNATIVE LOOP ALGEBRAS

We investigate polynomial identities on an alternative loop algebra and group identities on its (Moufang) unit loop. An alternative loop ring always satisfies a polynomial identity, whereas whether or not a unit loop satisfies a group identity depends on factors such as characteristic and centrality of certain kinds of idempotents.

Some examples of nil Lie algebras

Generalizing Petrogradsky`s construction, we give examples of infinite-dimensional nil Lie algebras of finite Gelfand-Kirillov dimension over any field of positive characteristic.