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| A Note on Restricted Representations of the Witt Superalgebras |
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Citation： |
Yufeng YAO,Bin SHU.A Note on Restricted Representations of the Witt Superalgebras[J].Chinese Annals of Mathematics B,2013,34(6):921~926 |
| Page view： 1574
Net amount： 1233 |
Authors： |
Yufeng YAO; Bin SHU; |
Foundation： |
National Natural Science Foundation of China (Nos. 11126062, 11201293,11226327, 11271130), and the Innovation Program of Shanghai Municipal Education Commission(Nos. 12ZZ038, 13YZ077). |
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| Abstract： |
Let F be an algebraically closed field of prime characteristic p > 3, and W(n)
the Witt superalgebra over F, which is the Lie superalgebra of superderivations of the
Grassmann algebra in n indeterminates. The dimensions of simple atypical modules in
the restricted supermodule category for W(n) are precisely calculated in this paper, and
thereby the dimensions of all simple modules can be precisely given. Moreover, the restricted
supermodule category for W(n) is proved to have one block. |
Keywords： |
Restricted Lie superalgebra, Witt superalgebra, Restricted representation,
Atypical weight |
Classification： |
17B10, 17B20, 17B50 |
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