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arXiv · 1801.03677

Algebras with irreducible module varieties II: Two vertex case

Grzegorz Bobiński·Jan Schröer
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Abstract

We call a finite-dimensional K-algebra A geometrically irreducible if for all d all connected components of the affine scheme of d-dimensional A-modules are irreducible. We prove that a geometrically irreducible algebra with exactly two simple modules has to be of a very special form, which we describe. Based on this result we prove that every minimal geometrically irreducible algebra without shortcuts in its Gabriel quiver has at most two simple modules.

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Grzegorz Bobiński, Jan Schröer. 2018-01-11. Algebras with irreducible module varieties II: Two vertex case. https://arxiv.org/abs/1801.03677

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