Algebraic entropy of amenable group actions

Simone Virili

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arXiv · 1410.8306

Algebraic entropy of amenable group actions

Simone Virili

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Abstract

Let $R$ be a ring, let $G$ be an amenable group and let $R\ast G$ be a crossed product. The goal of this paper is to construct, starting with a suitable additive function $L$ on the category of left modules over $R$, an additive function on a subcategory of the category of left modules over $R\ast G$, which coincides with the whole category if $L({}_RR) <\infty$. This construction can be performed using a dynamical invariant associated with the original function $L$, called algebraic $L$-entropy. We apply our results to two classical problems on group rings: the Stable Finiteness and the Zero-Divisors Conjectures.

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BibTeX RIS

Simone Virili. 2014-10-30. Algebraic entropy of amenable group actions. https://arxiv.org/abs/1410.8306

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