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arXiv · 2606.27879

The brick chain complexity of an artin algebra

Claus Michael Ringel
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Abstract

We consider the category of finitely generated modules over an artin algebra $A$. It is known that any module $M$ has a brick chain filtration. We say that M has brick chain complexity at most $t$ provided $M$ has a brick chain filtration of length at most $t$. The brick chain complexity of A is by definition the supremum of the brick chain complexity of the indecomposable $A$-modules. The aim of this note is to calculate the brick chain complexity for some algebras. We will exhibit algebras with arbitrarily large brick chain complexity.

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Claus Michael Ringel. 2026-06-26. The brick chain complexity of an artin algebra. https://arxiv.org/abs/2606.27879

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