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

Published online by Cambridge University Press:  09 April 2009

Wende Liu
Affiliation:
Department of MathematicsHarbin Normal UniversityHarbin 150080ChinaandDepartment of MathematicsNortheast Normal UniversityChangchun 130024China e-mail: [email protected]
Yongzheng Zhang
Affiliation:
Department of MathematicsHarbin Normal UniversityHarbin 150080China e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2005

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