Irreducible complex skew-Berger algebras

TL;DR

This paper classifies irreducible skew-Berger algebras, which are special Lie algebras satisfying the Bianchi identity, and interprets them as complex Berger superalgebras within the general linear superalgebra.

Contribution

It provides a complete classification of irreducible skew-Berger algebras, linking them to complex Berger superalgebras in the context of Lie superalgebra theory.

Findings

Classification of irreducible skew-Berger algebras completed

Connection established between skew-Berger algebras and Berger superalgebras

Provides structural insights into complex Lie algebra representations

Abstract

Irreducible skew-Berger algebras $\g\subset\gl(n,\Co)$, i.e. algebras spanned by the images of the linear maps $R:\odot^2\Co^n\to\g$ satisfying the Bianchi identity, are classified. These Lie algebras can be interpreted as irreducible complex Berger superalgebras contained in $\gl(0|n,\Co)$.