Classification of linearly compact simple rigid superalgebras
Nicoletta Cantarini, Victor G. Kac
TL;DR
This paper classifies all linearly compact simple rigid superalgebras, extending the concept beyond Lie and Jordan superalgebras to include new series and exceptional cases.
Contribution
It provides a complete classification of linearly compact simple anti-commutative and commutative rigid superalgebras, including new series and exceptional superalgebras.
Findings
Classified all linearly compact simple anti-commutative superalgebras
Classified all linearly compact simple commutative superalgebras
Identified new series and exceptional superalgebras
Abstract
The notion of an anti-commutative (resp. commutative) rigid superalgebra is a natural generalisation of the notion of a Lie (resp. Jordan) superalgebra. Intuitively rigidity means that small deformations of the product under 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 twenty two exceptional superalgebras (resp. ten exceptional superalgebras).
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons