Module categories over affine group schemes
Shlomo Gelaki
Technion - Israel Institute of Technology, Haifa, Israel
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Abstract
Let be an algebraically closed field of characteristic . Let be an affine group scheme over . We classify the indecomposable exact module categories over the rigid tensor category of coherent sheaves of finite dimensional -vector spaces on , in terms of - equivariant coherent sheaves on . We deduce from it the classification of indecomposable geometrical module categories over Rep. When is finite, this yields the classification of
all
indecomposable exact module categories over the finite tensor category Rep. In particular, we obtain a classification of twists for the group algebra of a finite group scheme . Applying this to , where is a finite dimensional -Lie algebra over with positive characteristic, produces (new) finite dimensional noncommutative and noncocommutative triangular Hopf algebras in positive characteristic. We also introduce and study group scheme theoretical categories, and study isocategorical finite group schemes.
Cite this article
Shlomo Gelaki, Module categories over affine group schemes. Quantum Topol. 6 (2015), no. 1, pp. 1–37
DOI 10.4171/QT/59