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 . Let be an affine supergroup scheme over k. We classify the indecomposable exact module categories over the tensor category of (coherent sheaves of) finite dimensional -supermodules in terms of -equivariant coherent sheaves on . We deduce from it the classification of indecomposable geometrical module categories over . When is finite, this yields the classification of all indecomposable exact module categories over the finite tensor category . In particular, we obtain a classification of twists for the supergroup algebra of a finite supergroup scheme , 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
令k为特征0的代数闭合域或。让是k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 有限维(相干滑轮)的 -supermodules在 等变相干滑轮 。我们据此推导了不可分解几何模块类别的分类。什么时候是有限的,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。特别是,我们获得了超群代数的扭曲分类 有限超群方案 ,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。