Irreducible continuous representations of the simple linearly compact n -Lie superalgebra of type S

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 Sn and continuous representations of the Lie algebra of Cartan type S, on which some two-sided ideal acts trivially.