Irreducible Continuous Representations of the Simple Linearly Compact n-Lie Superalgebra of type $S$

TL;DR

This paper classifies all irreducible continuous representations of a specific simple linearly compact n-Lie superalgebra of type S, establishing a correspondence with representations of the Lie algebra of Cartan type S.

Contribution

It provides the first complete classification of irreducible continuous representations for this class of n-Lie superalgebras, linking them to Lie algebra representations.

Findings

Classification of all irreducible continuous representations achieved.

Establishment of a bijective correspondence with Lie algebra representations.

Identification of the trivial action of a two-sided ideal in the classification process.

Abstract

In the present paper we classify all irreducible continuous representations of the simple linearly compact n-Lie superalgebra of type S. The classification is based on a bijective correspondence between the continuous representations of the n-Lie algebras S^n and continuous representations of the Lie algebra of Cartan type S, on which some two-sided ideal acts trivially.