Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields

TL;DR

This paper proves that the only Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields are trivial, using Z-grading and transitivity properties.

Contribution

It establishes the triviality of Hom-Lie superalgebra structures on exceptional simple Lie superalgebras, a result not previously known.

Findings

Only trivial Hom-Lie superalgebra structures exist on these algebras

Utilizes Z-grading and transitivity to analyze structures

Focuses on 0-th and -1-st Z-components for proof

Abstract

In this paper, the Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields are studied. Taking advantage of the Z-grading structures and the transitivity, we prove that there is only the trivial Hom-Lie superalgebra structures on exceptional simple Lie superalgebras. Our proof is obtained by studying the Hom-Lie superalgebra structures on their 0-th and -1-st Z-components.