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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.

Torsion units in group rings.

Vikas Bist (1992)

Publicacions Matemàtiques

Let U(RG) be the unit group of the group ring RG. In this paper we study group rings RG whose support elements of every torsion unit are torsion, where R is either the ring of integers Z or a field K.

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