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Finite-dimensional odd Hamiltonian superalgebras over a field of prime characteristic

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  09 April 2009

Wende Liu  and
Yongzheng Zhang
Wende Liu
Affiliation:
Department of MathematicsHarbin Normal UniversityHarbin 150080ChinaandDepartment of MathematicsNortheast Normal UniversityChangchun 130024China e-mail: wendeliu@sohu.com
Yongzheng Zhang
Affiliation:
Department of MathematicsHarbin Normal UniversityHarbin 150080China e-mail: zhyz@nenu.edu.cn
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Abstract

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Let ℋ(m;t) be the finite-dimensional odd Hamiltonian superalgebra over a field of prime characteristic. By determining ad-nilpotent elements in the even part, the natural filtration of ℋ (m;t) is proved to be invariant in the following sense: If ϕ: ℋ (m;t) → ℋ (m′t′) is an isomorphism then ϕ(ℋ(m;t)i) = ℋ (m′ t′) i for all i ≥ –1. Using the result, we complete the classification of odd Hamiltonian superalgebras. Finally, we determine the automorphism group of the restricted odd Hamiltonian superalgebra and give further properties.

MSC classification

Secondary: 17B50: Modular Lie (super)algebras 17B40: Automorphisms, derivations, other operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 1 , August 2005 , pp. 113 - 130
Copyright
Copyright © Australian Mathematical Society 2005

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