Support varieties for transporter category algebras

• Autores: Fei Xu
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 218, Nº 4, 2014, págs. 583-601
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2013.07.006
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• Resumen

  • Let G be a finite group. Over any finite G-poset P we may define a transporter category as the corresponding Grothendieck construction. The classifying space of the transporter category is the Borel construction on the G-space BP, while the k-category algebra of the transporter category is the (Gorenstein) skew group algebra on the G-algebra kP.

    We introduce a support variety theory for the category algebras of transporter categories.

    It extends Carlson�s support variety theory on group cohomology rings to equivariant cohomology rings. In the mean time it provides a class of (usually non selfinjective) algebras to which Snashall�Solberg�s (Hochschild) support variety theory applies. Various properties will be developed. Particularly we establish a Quillen stratification for modules.