On generic bricks over tame algebras

2024/08/28 by R. Bautista, E. Pérez, Bautista, R. +3 · 3 citations
Computer Science · Engineering · Mathematics · #16E30 #16E45 #16W50 #18E10 #18E30 #Advanced Algebra and Logic #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2408.16127

openalex publication_date 2024/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if Λ is a tame finite-dimensional algebra over an algebraically closed field and G is a generic Λ-module, then G is a generic brick if and only if it determines a one-parameter family of bricks with the same dimension. In particular, we obtain that Λ admits a generic brick if and only if Λ is brick-continuous.

Cited by

• Incidence algebras and beyond: brick-continuity and generic bricks
• Infinite string bricks and Sturmian words over some gentle algebras
• On the bricks (Schur representations) of finite dimensional algebras

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