Skew group algebras of piecewise hereditary algebras are piecewise hereditary

• Autores: Julie Dionne, Marcelo Lanzilotta, David Smith
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 213, Nº 2, 2009, págs. 241-249
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2008.06.010
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• Resumen

  • We show that the main results of Happel�Rickard�Schofield (1988) and Happel�Reiten�Smalø (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.