Tame hereditary path algebras and amenability

Eckert, Sebastian

doi:10.1112/blms.12822

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Tame hereditary path algebras and amenability

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Eckert, Sebastian
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1112/blms.12822
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https://doi.org/10.48550/arXiv.1808.02092
(Preprint)

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Eckert_Tame hereditary path algebras and amenability_2023.pdf
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Eckert, S. (2023). Tame hereditary path algebras and amenability. Bulletin of the London Mathematical Society, 55(4), 1837-1856. doi:10.1112/blms.12822.

Cite as: https://hdl.handle.net/21.11116/0000-000C-E757-E

Abstract

In this note we revisit the notion of amenable representation type introduced by Gábor Elek. We show that tame hereditary path algebras of quivers of extended Dynkin type over any field k are of amenable type. This verifies a conjecture of Elek, which draws similarities to the tame-wild dichotomy, for another class of tame algebras. We also show that path algebras of wild acyclic quivers over finite fields are not amenable.