Filtration, automorphisms and classification of the infinite dimensional odd Contact superalgebras superalgebras

TL;DR

This paper investigates the automorphism group of infinite-dimensional odd Contact superalgebras over fields with characteristic greater than 2, establishing invariance properties, automorphism criteria, and classifying all such superalgebras up to isomorphism.

Contribution

It proves the invariance of the principal filtration under automorphisms, characterizes automorphisms by their action on a specific component, and classifies all odd Contact superalgebras up to isomorphism.

Findings

Principal filtration is invariant under automorphisms.

Automorphisms are determined by their action on the -1 component.

Complete classification of odd Contact superalgebras up to isomorphism.

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.