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Graded singularity category of Gorenstein algebras with levelled Beilinson algebras

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Graded singularity category of Gorenstein algebras with levelled Beilinson algebras
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16
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Abstract
Our goal is to find conditions on a noetherian AS-regular algebra A and an idempotent e∈A for which the graded singularity category Singgr(eAe) admits a tilting object. Of particular interest is the situation in which A is a graded skew-group algebra S#G, where S is the polynomial ring in n variables and G<SL(n,k) is finite, and e=1|G|∑g∈Gg, so that eAe≅SG. A tilting object was found by Amiot, Iyama and Reiten in the case where A has Gorenstein parameter 1. Generalizing the work of Iyama and Takahashi, Mori and Ueyama obtained a tilting object in Singgr(SG), provided that S is a noetherian AS-regular Koszul algebra generated in degree 1 and G has homological determinant 1. In this talk, we will discuss certain silting objects and then specialise to the setting in which the Beilinson algebra is a levelled algebra, giving a generalisation of the result of Mori and Ueyama.