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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.

The density of representation degrees

Martin Liebeck, Dan Segal, Aner Shalev (2012)

Journal of the European Mathematical Society

For a group G and a positive real number x , define d G ( x ) to be the number of integers less than x which are dimensions of irreducible complex representations of G . We study the asymptotics of d G ( x ) for algebraic groups, arithmetic groups and finitely generated linear groups. In particular we prove an “alternative” for finitely generated linear groups G in characteristic zero, showing that either there exists α > 0 such that d G ( x ) > x α for all large x , or G is virtually abelian (in which case d G ( x ) is bounded).

Currently displaying 761 – 780 of 995