Multiplicative Hom-Lie superalgebra structures on infinite dimensional simple Lie superalgebras of vector fields

TL;DR

This paper proves that infinite dimensional simple Lie superalgebras of vector fields in characteristic zero admit only the trivial multiplicative Hom-Lie superalgebra structure, highlighting their rigidity.

Contribution

It establishes the uniqueness of the multiplicative Hom-Lie superalgebra structure on these infinite dimensional Lie superalgebras.

Findings

Only the trivial multiplicative Hom-Lie superalgebra structure exists

Infinite dimensional simple Lie superalgebras are rigid under such structures

No nontrivial multiplicative Hom-Lie superalgebra structures are possible

Abstract

This paper considers the multiplicative Hom-Lie superalgebra structures on infinite dimensional simple Lie superalgebras of vector fields with characteristic zero. The main result is that there is only the multiplicative Hom-Lie superalgebra structure on these Lie superalgebras.