Finitistic dimensions and piecewise hereditary property of skew group algebras

2013/04/01 by Liping Li, Li, Liping
Mathematics · #16E10 #16G10 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16E10 #msc:16G10

paper · pdf · doi:10.48550/arxiv.1304.0482

A technical mistake was corrected

arxiv created 2014/04/16 · arxiv updated 2014/04/18

Abstract

Let Λ be a finite dimensional algebra and G be a finite group whose elements act on Λ as algebra automorphisms. Under the assumption that Λ has a complete set E of primitive orthogonal idempotents, closed under the action of a Sylow p-subgroup S \leqslant G. If the action of S on E is free, we show that the skew group algebra ΛG and Λ have the same finitistic dimension, and have the same strong global dimension if the fixed algebra Λ^S is a direct summand of the Λ^S-bimodule Λ. Using a homological characterization of piecewise hereditary algebras proved by Happel and Zacharia, we deduce a criterion for ΛG to be piecewise hereditary.

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