Filtration, automorphisms, and classification of infinite-dimensional odd contact superalgebras

doi:10.1007/s11464-012-0185-6

Front Math Chin

2013, Vol. 8

Issue (1) : 203-216 https://doi.org/10.1007/s11464-012-0185-6

RESEARCH ARTICLE

Filtration, automorphisms, and classification of infinite-dimensional odd contact superalgebras

Jixia YUAN¹, Wende LIU²(

)

1. School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China; 2. School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China

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Abstract

The principal filtration of the infinite-dimensional odd contact Lie superalgebra over a field of characteristic p>2 is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and determining certain invariants such as subalgebras generated by some ad-nilpotent elements. Then, it is proved that two automorphisms coincide if and only if they coincide on the -1 component with respect to the principal grading. Finally, all the odd contact superalgebras are classified up to isomorphisms.

Keywords Lie superalgebra filtration automorphism classification

Corresponding Author(s): LIU Wende,Email:wendeliu@ustc.edu.cn

Issue Date: 01 February 2013

Cite this article:

Jixia YUAN,Wende LIU. Filtration, automorphisms, and classification of infinite-dimensional odd contact superalgebras[J]. Front Math Chin, 2013, 8(1): 203-216.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-012-0185-6
https://academic.hep.com.cn/fmc/EN/Y2013/V8/I1/203

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