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arXiv · 2211.06563

Amenability of monomial algebras, minimal subshifts and free subalgebras

Jason P. Bell·Be'eri Greenfeld
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Abstract

We give a combinatorial characterization of amenability of monomial algebras and prove the existence of monomial Folner sequences, answering a question due to Ceccherini-Silberstein and Samet-Vaillant. We then use our characterization to prove that over projectively simple monomial algebras, every module is exhaustively amenable; we conclude that convolution algebras of minimal subshifts admit the same property. We deduce that any minimal subshift of positive entropy gives rise to a graded algebra which does not satisfy an extension of Vershik's conjecture on amenable groups, proposed by Bartholdi. Finally, we show that non-amenable monomial algebras must contain noncommutative free subalgebras. Examples are given to emphasize the sharpness and necessity of the assumptions in our results.

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BibTeXRIS

Jason P. Bell, Be'eri Greenfeld. 2022-11-12. Amenability of monomial algebras, minimal subshifts and free subalgebras. https://arxiv.org/abs/2211.06563

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