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Journal of Lie Theory 30 (2020), No. 1, 145--154
Copyright Heldermann Verlag 2020

Block Degeneracy for Graded Lie Superalgebras of Cartan Type

Ke Ou
Dept. of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, P. R. China

Let K be an algebraically closed field of characteristic p > 0. In this short note, we illustrate a class of Lie superalgebras over K such that the category of restricted supermodules is of one block. As an application, if p > 3 and g is a graded restricted Cartan type Lie superalgebra of type W, S and H, then the category of restricted supermodules of g is of one block.

Keywords: Lie superalgebra of Cartan type, block, restricted supermodule, baby Verma module.

MSC: 17B10, 17B35, 17B50, 17B70.

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