Algebras with irreducible module varieties I

Grzegorz Bobiński; Jan Schröer

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arXiv · 1709.05841

Algebras with irreducible module varieties I

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 show that the geometrically irreducible algebras without loops (this includes all algebras of finite global dimension) are the hereditary algebras. We also show that truncated polynomial rings are the only geometrically irreducible local algebras. Finally, we formulate a conjectural classification of all geometrically irreducible algebras.

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Grzegorz Bobiński, Jan Schröer. 2017-09-18. Algebras with irreducible module varieties I. https://arxiv.org/abs/1709.05841

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