The kantor construction of jordan superalgebras

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.