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Mathematics > Rings and Algebras

arXiv:math/0703507 (math)
[Submitted on 17 Mar 2007 (v1), last revised 2 May 2008 (this version, v3)]

Title:Skew group algebras of piecewise hereditary algebras are piecewise hereditary

Authors:Julie Dionne, Marcelo Lanzilotta, David Smith
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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.
Comments: 13 pages, typos corrected. To appear in J. Pure Appl. Algebra
Subjects: Rings and Algebras (math.RA); Representation Theory (math.RT)
MSC classes: 16S35, 18E30
Cite as: arXiv:math/0703507 [math.RA]
  (or arXiv:math/0703507v3 [math.RA] for this version)
  https://doi.org/10.48550/arXiv.math/0703507

Submission history

From: David Smith [view email]
[v1] Sat, 17 Mar 2007 00:03:43 UTC (29 KB)
[v2] Thu, 20 Sep 2007 19:48:58 UTC (29 KB)
[v3] Fri, 2 May 2008 18:52:16 UTC (19 KB)
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