Militaru, G.
Published in
Algebras and Representation Theory

Let H be a bialgebra and H LH be the category of Long H-dimodules defined, for a commutative and co-commutative H, by F. W. Long and studied in connection with the Brauer group of a so-called H-dimodule algebra. For a commutative and co-commutative H, H LH =H YDH (the category of Yetter–Drinfel'd modules), but for an arbitrary H, the categories H L...

Izhboldin, Oleg T. Karpenko, Nikita A.
Published in
Algebras and Representation Theory

A field extension L / F is called excellent if, for any quadratic form φ over F, the anisotropic part (φL)an of φ over L is defined over F; L / F is called universally excellent if L ⋅ E / E is excellent for any field extension E / F. We study the excellence property for a generic splitting field of a central simple F-algebra. In particular, we sho...

Altmann, Klaus Hille, Lutz
Published in
Algebras and Representation Theory

Let Q be a finite quiver without oriented cycles. Denote by U → ℳ(Q) the fine moduli space of stable thin sincere representations of Q with respect to the canonical stability notion. We prove Extℳ(Q)l (U, U) = 0 for all l > 0 and compute the endomorphism algebra of the universal bundle U. Moreover, we obtain a necessary and sufficient condition for...

Daele, A. Van Zhang, Y. H.
Published in
Algebras and Representation Theory

In this paper, we introduce a generalized Hopf Galois theory for regular multiplier Hopf algebras with integrals, which might be viewed as a generalization of the Hopf Galois theory of finite-dimensional Hopf algebras. We introduce the notion of a coaction of a multiplier Hopf algebra on an algebra. We show that there is a duality for actions and c...

Green, James A.
Published in
Algebras and Representation Theory

The ‘discrete series’ characters of the finite general linear group GL(n, q) are expressed as uniquely defined integral linear combinations of characters induced from linear characters on certain subgroups Hd, n of GL(n, q). The coefficients in these linear combinations are determined (for all n, q) by a family of polynomials rλ(T) ∈ Z[T] indexed b...

Chen, Huanyin
Published in
Algebras and Representation Theory

We prove that every exchange ring with primitive factors Artinian is clean. Also, it is shown that for exchange rings with Artinian primitive factors, the following are equivalent: (1) Every element in R is a sum of two units. (2) There exist α, β ∈ U(R) such that α + β = 1. (3) R does not have Z / 2 Z as a homomorphic image. Finally, we prove that...

Linckelmann, Markus
Published in
Algebras and Representation Theory

We develop the notion of a cohomology ring of blocks of finite groups and study its basic properties by means of transfer maps between the Hochschild cohomology rings of symmetric algebras associated with bounded complexes of finitely generated bimodules which are projective on either side.

Ene, Viviana Popescu, Dorin
Published in
Algebras and Representation Theory

Let k be an algebraically closed field of characteristic ≠ 3 and i, j, t some positive integers such that 1 ≤ i

Vancliff, Michaela
Published in
Algebras and Representation Theory

A family of flat deformations of a commutative polynomial ring S on n generators is considered, where each deformation B is a twist of S by a semisimple, linear automorphism σ of ℙn−1, such that a Poisson bracket is induced on S. We show that if the symplectic leaves associated with this Poisson structure are algebraic, then they are the orbits of ...

Ksir, Amy E.
Published in
Algebras and Representation Theory

Let W be a Weyl group and P ⊂ W, a parabolic subgroup. In this paper, we give the decomposition of the permutation representation IndPW 1 into irreducibles for each exceptional W and maximal parabolic P. We find that there is an 'extra' common irreducible component which appears for exceptional groups and not for classical groups. This work is moti...