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Module categories over affine supergroup schemes
Journal of Pure and Applied Algebra ( IF 0.8 ) Pub Date : 2021-02-15 , DOI: 10.1016/j.jpaa.2021.106711
Shlomo Gelaki

Let k be an algebraically closed field of characteristic 0 or p>2. Let G be an affine supergroup scheme over k. We classify the indecomposable exact module categories over the tensor category sCohf(G) of (coherent sheaves of) finite dimensional O(G)-supermodules in terms of (H,Ψ)-equivariant coherent sheaves on G. We deduce from it the classification of indecomposable geometrical module categories over sRep(G). When G is finite, this yields the classification of all indecomposable exact module categories over the finite tensor category sRep(G). In particular, we obtain a classification of twists for the supergroup algebra kG of a finite supergroup scheme G, and then combine it with [7, Corollary 4.1] to classify finite dimensional triangular Hopf algebras with the Chevalley property over k.



中文翻译:

仿射超群方案的模块类别

k为特征0的代数闭合域或p>2个。让Gk上的一个仿射超群方案。我们将张量类别中不可分解的确切模块类别分类ohFG 有限维(相干滑轮)的 ØG-supermodules在 HΨ等变相干滑轮 G。我们据此推导了不可分解几何模块类别的分类回复G。什么时候G是有限的,这将得出有限张量类别上所有不可分解的精确模块类别的分类回复G。特别是,我们获得了超群代数的扭曲分类ķG 有限超群方案 G,然后将其与[7,Corollary 4.1]结合,对具有在k上的Chevalley属性的有限维三角Hopf代数进行分类

更新日期:2021-03-09
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