$\delta$-derivations of classical Lie superalgebras

TL;DR

This paper investigates the $ extdelta$-derivations of classical Lie superalgebras, establishing conditions for their existence and fully characterizing the structure of 1/2-derivations, thereby advancing understanding of their algebraic properties.

Contribution

It proves that nonzero $ extdelta$-derivations occur only for specific values and completely describes the structure of 1/2-derivations in classical Lie superalgebras.

Findings

Nonzero $ extdelta$-derivations only for $ extdelta=0,1/2,1$

Complete characterization of 1/2-derivations

Enhanced understanding of algebraic structure of Lie superalgebras

Abstract

We consider the $\delta$-derivations of classical Lie superalgebras and prove that these superalgebras admit nonzero $\delta$-derivations only when $\delta = 0,1/2,1$. The structure of $1/2$-derivations for classical Lie superalgebras is completely determined.