Skew group algebras of piecewise hereditary algebras are piecewise hereditary

2007/03/17 by Julie Dionne, Dionne, Julie, Marcelo Lanzilotta +4
Computer Science · Mathematics · #16S35 #18E30 #Advanced Algebra and Logic #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #math.RT #msc:16S35 #msc:18E30

paper · pdf · doi:10.48550/arxiv.math/0703507

13 pages, typos corrected. To appear in J. Pure Appl. Algebra

openalex publication_date 2007/03/17 · arxiv created 2008/05/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the main results of Happel-Rickard-Schofield (1988) and Happel-Reiten-Smalo (1996) on piecewise hereditary algebras are coherent with the notion of group action on an algebra. Then, we take advantage of this compatibility and show that if G is a finite group acting on a piecewise hereditary algebra A over an algebraically closed field whose characteristic does not divide the order of G, then the resulting skew group algebra A[G] is also piecewise hereditary.

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