Quadratic Lie Superalgebras Generalized by Balinsky–Novikov Superalgebras
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Balinsky–Novikov superalgebras were introduced by Balinsky for constructing super-Vira-soro type Lie superalgebras. In this paper, we give sufficient and necessary conditions for a Lie superalgebra generalized by a Balinsky–Novikov superalgebra with dimension 2|2 to be a quadratic Lie superalgebra.
KeywordsBalinsky–Novikov superalgebra Lie superalgebra quadratic Lie superalgebra
MR(2010) Subject Classification17B65 17A70
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The authors are very grateful for the helpful comments and suggestions from the referees.