Classification of Linearly Compact Simple Rigid Superalgebras

Abstract

The notion of an anti-commutative (resp. commutative) rigid superalgebra is a natural generalization of the notion of a Lie (resp. Jordan) superalgebra. Intuitively, rigidity means that small deformations of the product under the action of the structural group produce an isomorphic algebra. In this paper, we classify all linearly compact simple anti-commutative (resp. commutative) rigid superalgebras. Beyond Lie (resp. Jordan) superalgebras, the complete list includes four series and 22 exceptional superalgebras (resp. 10 exceptional superalgebras).