On $\mathrm{ID}^{*}$-superderivations of Lie superalgebras

TL;DR

This paper investigates the structure of a specific class of superderivations in Lie superalgebras, providing bounds on their superdimension and characterizations for certain nilpotent cases using matrix methods.

Contribution

It offers an upper bound for the superdimension of $ ext{ID}^*$-superderivations and characterizes these superderivations for nilpotent Lie superalgebras of class 2 and model filiform types.

Findings

Upper bound for superdimension of $ ext{ID}^*$-superderivations

Characterization of $ ext{ID}^*$-superderivations for class 2 nilpotent Lie superalgebras

Characterization for model filiform Lie superalgebras

Abstract

Let $L$ be a Lie superalgebra over a field of characteristic different from $2,3$ and write $\mathrm{ID}^{*}(L)$ for the Lie superalgebra consisting of superderivations mapping $L$ to $L^{2}$ and the central elements to zero. In this paper we first give an upper bound for the superdimension of $\mathrm{ID}^{*}(L)$ by means of linear vector space decompositions. Then we characterize the $\mathrm{ID}^{*}$-superderivation superalgebras for the nilpotent Lie superalgebras of class 2 and the model filiform Lie superalgebras by methods of block matrices.