Graded blocks of group algebras with dihedral defect groups

Dusko Bogdanic

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2010 Mathematics Subject Classification: 16R10, 16W55, 15A75. We survey some recent results on graded Gelfand-Kirillov dimension of PI-algebras over a field F of characteristic 0. In particular, we focus on verbally prime algebras with the grading inherited by that of Vasilovsky and upper triangular matrices, i.e., UTn(F), UTn(E) and UTa,b(E), where E is the infinite dimensional Grassmann algebra.

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The correspondence between the category of modules over a graded algebra and the category of graded modules over its Yoneda algebra was studied in [8] by means of $A_{\infty}$ algebras; this relation is very well understood for Koszul algebras (see for example [5],[6]). It is of interest to look for cases such that there exists a duality generalizing the Koszul situation. In this paper we will study N-Koszul algebras [1], [7], [9] for which such a duality exists.

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