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Algebras generated by odd derivations. (English) Zbl 1369.17031

Summary: Given an associative supercommutative algebra equipped with an odd derivation, one considers the space of vector fields it defines, and shows, under suitable hypothesis, they form a Jordan superalgebra; in contrast with the Lie superalgebras of Virasoro type constructed from even derivations. Relations with anti-Lie algebras studied by Ovsienko and collaborators are then shown.

MSC:

17C70 Super structures
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
81Q60 Supersymmetry and quantum mechanics
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