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Tame tensor products of algebras

Zbigniew Leszczyński, Andrzej Skowroński (2003)

Colloquium Mathematicae

With the help of Galois coverings, we describe the tame tensor products A ⊗ K B of basic, connected, nonsimple, finite-dimensional algebras A and B over an algebraically closed field K. In particular, the description of all tame group algebras AG of finite groups G over finite-dimensional algebras A is completed.

The adjoint representation of group algebras and enveloping algebras.

Donald S. Passman (1992)

Publicacions Matemàtiques

In this paper we study the Hopf adjoint action of group algebras and enveloping algebras. We are particularly concerned with determining when these representations are faithful. Delta methods allow us to reduce the problem to certain better behaved subalgebras. Nevertheless, the problem remains open in the finite group and finite-dimensional Lie algebra cases.

The Bass conjecture and growth in groups

Anders Karlsson, Markus Neuhauser (2004)

Colloquium Mathematicae

We discuss Bass's conjecture on the vanishing of the Hattori-Stallings rank from the viewpoint of geometric group theory. It is noted that groups without u-elements satisfy this conjecture. This leads in particular to a simple proof of the conjecture in the case of groups of subexponential growth.

The converse of Schur's Lemma in group rings

M. Alaoui, A. Haily (2006)

Publicacions Matemàtiques

In this paper, we study the structure of group rings by means of endomorphism rings of their modules. The main tools used here, are the subrings fixed by automorphisms and the converse of Schur's lemma. Some results are obtained on fixed subrings and on primary decomposition of group rings.

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