Journal of Lie Theory 21 (2011), No. 3, 729--754
Copyright Heldermann Verlag 2011
Finite-Dimensional Odd Contact Superalgebras over a Field of Prime Characteristic
Yan Chen
School of Mathematical Sciences, Harbin Normal University, Harbin 150025, P. R. China
Wende Liu
School of Mathematical Sciences, Harbin Normal University, Harbin 150025, P. R. China
wendeliu@ustc.edu.cn
Let g be any finite-dimensional odd Contact superalgebra over a field of prime characteristic. By means of determining the minimal dimensions of image spaces of certain inner superderivations, it is proved that the principal filtration of g is invariant under the automorphisms of g. Then, the parameters by which g is defined are proved to be intrinsic and thereby the odd Contact superalgebras are classified up to isomorphisms. Furthermore, the restrictedness of g is determined and the automorphism group of g in restrictedness case is proved to be isomorphic to the admissible automorphism group of the underlying superalgebra of g under a concrete isomorphism Φ. Further properties of Φ are given and as an application, the results above are used to discuss the p-characters of the irreducible representations for g.
Keywords: Odd contact superalgebra, filtration, automorphism, character.
MSC: 17B50, 17B4
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