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FINITISTIC DIMENSIONS AND PIECEWISE HEREDITARY PROPERTY OF SKEW GROUP ALGEBRAS

Part of: Homological methods Representation theory of rings and algebras

Published online by Cambridge University Press:  18 December 2014

LIPING LI
LIPING LI*
Affiliation:
Department of Mathematics, University of California, Riverside, CA, USA, 92521 e-mail: [email protected]
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Abstract

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

MSC classification

Primary: 16G10: Representations of Artinian rings
Secondary: 16E10: Homological dimension
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 3 , September 2015 , pp. 509 - 517
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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