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arXiv · 2607.25443

Incidence algebras and beyond: brick-continuity and generic bricks

Edoardo Tacchetti
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Abstract

We will show that the twelve families of minimally representation-infinite incidence algebras are brick-continuous and admit a generic brick, which will be explicitly constructed. After that, reversing the reduction process between posets, we will show that any representation-infinite incidence algebra is brick-continuous and admits a generic brick, which can be explicitly computed using what will be called ``extension functors''. Lastly, a method to apply these results to a broader class of algebras is given.

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Edoardo Tacchetti. 2026-07-28. Incidence algebras and beyond: brick-continuity and generic bricks. https://arxiv.org/abs/2607.25443

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