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.

Arithmetic fuchsian groups and space time block codes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A contribuition to the study of channel coding in wireless communication systems

Pós-graduação em Engenharia Elétrica - FEIS

Class Notes for Math 901/902: Abstract Algebra, Instructor Tom Marley

Topics include: Free groups and presentations; Automorphism groups; Semidirect products; Classification of groups of small order; Normal series: composition, derived, and solvable series; Algebraic field extensions, splitting fields, algebraic closures; Separable algebraic extensions, the Primitive Element Theorem; Inseparability, purely inseparable extensions; Finite fields; Cyclotomic field extensions; Galois theory; Norm and trace maps of an algebraic field extension; Solvability by radicals, Galois' theorem; Transcendence degree; Rings and modules: Examples and basic properties; Exact sequences, split short exact sequences; Free modules, projective modules; Localization of (commutative) rings and modules; The prime spectrum of a ring; Nakayama's lemma; Basic category theory; The Hom functors; Tensor products, adjointness; Left/right Noetherian and Artinian modules; Composition series, the Jordan-Holder Theorem; Semisimple rings; The Artin-Wedderburn Theorem; The Density Theorem; The Jacobson radical; Artinian rings; von Neumann regular rings; Wedderburn's theorem on finite division rings; Group representations, character theory; Integral ring extensions; Burnside's paqb Theorem; Injective modules.

FREE GROUP ALGEBRAS IN DIVISION RINGS

Let k be an algebraically closed field of characteristic zero and let L be an algebraic function field over k. Let sigma : L -> L be a k-automorphism of infinite order, and let D be the skew field of fractions of the skew polynomial ring L[t; sigma]. We show that D contains the group algebra kF of the free group F of rank 2.

A SURVEY ON FREE OBJECTS IN DIVISION RINGS AND IN DIVISION RINGS WITH AN INVOLUTION

Let D be a division ring with center k, and let D-dagger be its multiplicative group. We investigate the existence of free groups in D-dagger, and free algebras and free group algebras in D. We also go through the case when D has an involution * and consider the existence of free symmetric and unitary pairs in D-dagger.

Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.

Wolbachia replication and host cell division in Aedes albopictus

Wolbachia pipientis is an obligate intracellular endosymbiont of a range of arthropod species. The microbe is best known for its manipulations of host reproduction that include inducing cytoplasmic incompatibility, parthenogenesis, feminization, and male-killing. Like other vertically transmitted intracellular symbionts, Wolbachiarsquos replication rate must not outpace that of its host cells if it is to remain benign. The mosquito Aedes albopictus is naturally infected both singly and doubly with different strains of Wolbachia pipientis. During diapause in mosquito eggs, no host cell division is believed to occur. Further development is triggered only by subsequent exposure of the egg to water. This study uses diapause in Wolbachia-infected Aedes albopictus eggs to determine whether symbiont replication slows or stops when host cell division ceases or whether it continues at a low but constant rate. We have shown that Wolbachia densities in eggs are greatest during embryonation and then decline throughout diapause, suggesting that Wolbachia replication is dependent on host cell replication.

The Rural Clinical Division: a student journey to rural medicine

Background: The University of Queensland has through an Australian Government initiative, established a Rural Clinical Division (RCD) at four regional sites in the southern and central Queensland. Over the fi rst four years of the existence of the RCD, an integrated package of innovative medical education has been developed. Method: The integrated aspects of the RCD program include: The Rural Medical Rotation: Every medical student undertakes an eight week rural rotation in Year 3. Year 3 and 4 MBBS - 100 students are currently spending one to two years in the rural school and demand is increasing. Interprofessional Education - Medical and Allied Health students attend lectures, seminars and workshops together and often share the same rural clinical placement. Rural health projects - allow students to undertake a project of benefi t to the rural community. Information Technology (IT) - the Clinical Discussion Board (CDB) and Personal Digital Assistants (PDA) demonstrate the importance of IT to medical students in the 21st century. Changing the Model of Medical Education - The Leichhardt Community Attachment Placement (LCAP), is a pilot study that resulted in the addition of three interns to the rural workforce. All aspects of the RCD are evaluated with surveys using both qualitative and quantitative free response questions, completed by all students regularly throughout the academic year. Results: Measures of impact include: Student satisfaction and quality of teaching surveys – 86-91% of students improved their clinical skills and understanding across all rotations. Academic results and progress – RCD students out-perform their urban colleagues. Intent to work in rural areas – 90% of students reported a greater interest in rural medicine. Intern numbers – rural / regional intern placements are increasing. Conclusions: The RCD proves to be a site for innovations all designed to help reach our primary goal of fostering increased recruitment of a rural medical workforce.

On super-RS algebra and Drinfeld realization of quantum affine superalgebras

We describe the realization of the super-Reshetikhin-Semenov-Tian-Shansky (RS) algebra in quantum affine superalgebras, thus generalizing the approach of Frenkel and Reshetikhin to the supersymmetric (and twisted) case. The algebraic homomorphism between the super-RS algebra and the Drinfeld current realization of quantum affine superalgebras is established by using the Gauss decomposition technique of Ding and Frenkel. As an application, we obtain Drinfeld realization of quantum affine superalgebra U-q [osp(1/2)((1))] and its degeneration - central extended super-Yangian double DY(h over bar) [osp(1/2)((1))].

Post-familial families and the domestic division of labour

This paper takes as its starting point recent claims by Beck-Gernsheim (2002) that we are living in an era of post-familial families. Beck-Gernsheim (2002) argues that our lives are no longer structured as they once were by tradition, class, religion and kin. Instead the family has become a transitional phase as individuals strive for fulfillment of personal goals and personal life projects. The demographic evidence to support these claims is clearly evident in relation to changing patterns of family formation and dissolution, as well as the movement of married women into paid employment. But what is less evident is a decline in traditional patterns of gender stratification within families. This paper uses recent national data from Australia to examine the relationship between post-familial status, as indicated by marital status and employment, and time spent on housework. The results show that gender is still a clear predictor of time spent on housework, but that within gender there is evidence that gender inequality may be declining in non-traditional households.

Anisotropic correlated electron model associated with the Temperley-Lieb algebra

We present an anisotropic correlated electron model on a periodic lattice, constructed from an R-matrix associated with the Temperley-Lieb algebra. By modification of the coupling of the first and last sites we obtain a model with quantum algebra invariance.