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Seminario di Algebra: Length functions of Grothendieck categories with applications to infinite group representations II

Venerdì 24 Ottobre 2014, ore 16:00 - Aula 2AB45 - Simone Virili

ARGOMENTI: Seminari

Venerdì 24 Ottobre 2014 alle ore 16:00 in aula 2AB45, Simone Virili, assegnista del nostro Dipartimento, terrà il seminario su argomenti della sua tesi di dottorato "Length functions of Grothendieck categories with applications to infinite group representations II"

Abstract
We start the second part showing that, for general groups, the answer to our main question is negative. This forces us to introduce the class of amenable groups and to restrict our attention to this class of groups.
Given a crossed product R*G, with G amenable, and a length function L of R-Mod we construct a suitable notion of algebraic L-entropy for left R*G modules and, using this "dynamical" invariant, we can partially answer to our main question in the positive.
In the last part of the seminar we apply this new notion of entropy to obtain new results on (generalized versions of) the Stable Finiteness and the Zero-Divisors Conjectures, introduced in the seventies by Kaplansky.

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