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.

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...

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

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...

Böhm, Gabriella
Published in
Algebras and Representation Theory

The theory of integrals is used to analyze the structure of Hopf algebroids. We prove that the total algebra of a Hopf algebroid is a separable extension of the base algebra if and only if it is a semi-simple extension and if and only if the Hopf algebroid possesses a normalized integral. It is a Frobenius extension if and only if the Hopf algebroi...

Buan, Aslak Bakke Solberg, Øyvind
Published in
Algebras and Representation Theory

The set of pure-injective cotilting modules over an artin algebra is shown to have a monoid structure. This monoid structure does not restrict down to a monoid structure on the finitely generated cotilting modules in general, but it does whenever the algebra is of finite representation type. Pure-injective cotilting modules are also constructed fro...