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

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

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