Automorphism groups of the finite dimensional special odd Hamiltonian superalgebras in prime characteristic

TL;DR

This paper investigates the automorphism groups of finite dimensional special odd Hamiltonian superalgebras over fields of prime characteristic, establishing their relationship with automorphism groups of underlying superalgebras and describing their structure.

Contribution

It characterizes the connection between automorphism groups of these superalgebras and their underlying structures, embedding one into the other and analyzing their normal series.

Findings

Automorphism groups are embedded into those of underlying superalgebras.

Normal series and homogeneous automorphism groups are explicitly determined.

The structure of automorphism groups is clarified in the prime characteristic setting.

Abstract

This paper is devoted to a study of the automorphism groups of three series of finite dimensional special odd Hamiltonian superalgebras $\mathfrak{g}$ over a field of prime characteristic. Our aim is to characterize the connections between the automorphism groups of $\mathfrak{g}$ and the automorphism groups of the corresponding underlying superalgebras. Precisely speaking, we embed the former into the later. Moreover, we determine the images of the normal series of the automorphism groups and homogeneous automorphism groups of $\mathfrak{g.}$