Superderivations for Modular Graded Lie Superalgebras of Cartan-type

TL;DR

This paper provides a comprehensive determination of superderivations for Cartan-type graded Lie superalgebras over fields with characteristic greater than 3, simplifying the analysis through a uniform reduction approach.

Contribution

It introduces a uniform method to determine superderivations, reducing infinite dimensional cases to finite and further to restricted cases, and fully characterizes outer superderivation algebras.

Findings

Superderivations are fully characterized for all eight families.

The reduction approach simplifies the analysis of infinite dimensional cases.

Outer superderivation algebras are explicitly determined.

Abstract

Superderivations for the eight families of finite or infinite dimensional graded Lie superalgebras of Cartan-type over a field of characteristic $p>3$ are completely determined by a uniform approach: The infinite dimensional case is reduced to the finite dimensional case and the latter is further reduced to the restrictedness case, which proves to be far more manageable. In particular, the outer superderivation algebras of those Lie superalgebras are completely determined.