Lie Superautomorphisms on Associative Algebras, II

TL;DR

This paper characterizes Lie superautomorphisms of prime associative superalgebras, showing they are generally of standard form except in specific low-dimensional cases, advancing understanding of superalgebra symmetries.

Contribution

It provides a complete classification of Lie superautomorphisms for central simple superalgebras, highlighting exceptions in dimensions 2 and 4.

Findings

Lie superautomorphisms are of standard form in most cases

Exceptions occur when the superalgebra dimension is 2 or 4

The result applies specifically to central simple superalgebras

Abstract

Lie superautomorphisms of prime associative superalgebras are considered. A definitive result is obtained for central simple superalgebras: their Lie superautomorphisms are of standard forms, except when the dimension of the superalgebra in question is 2 or 4.