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39. The kantor construction of jordan superalgebras

Author

Mccrimmon Kevin and King Daniel

Subjects
Pure mathematics, Poisson bracket, Algebra and Number Theory, Simple (abstract algebra), Mathematics::Quantum Algebra, Product (mathematics), Mathematics::Rings and Algebras, Dimension (graph theory), Type (model theory), Mathematics::Representation Theory, Superalgebra, Variable (mathematics), Mathematics
Abstract

Superalgebras J(F) of finite or infinite dimension obtained by the Kantor doubling process from dot-bracket superalgebras (F, ., x ) with a supercommutative, associative product . and a superbracket x are examined. Such a superalgebra is Jordan if and only if x is a Jordan superbracket and is simple if and only if (F, ., x) is simple. Superalgebras J(F) of vector type where D is a derivation of (F, .)) are special. Superalgebras J(F) for poisson brackets F on even and odd variables are exceptional except in the case of a single odd variable and no even variables.

Published
1992

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