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arXiv · 2001.04730

Quantity vs. size in representation theory

Jorge Vitória
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Abstract

In this note, we survey two instances in the representation theory of finite-dimensional algebras where the quantity of a type of structures is intimately related to the size of those same structures. More explicitly, we review the fact that (1) a finite-dimensional algebra admits only finitely many indecomposable modules up to isomorphism if and only if every indecomposable module is finite-dimensional; (2) the category of modules over a finite-dimensional algebra admits only finitely many torsion classes if and only if every torsion class is generated by a finite-dimensional module.

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Jorge Vitória. 2020-01-14. Quantity vs. size in representation theory. https://arxiv.org/abs/2001.04730

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