Abstract:
We show that the Jordan bracket on an associative commutative superalgebra is extendable to the superalgebra of fractions. In particular, we prove that a unital simple abelian Jordan superalgebra is embedded into a simple superalgebra of a Jordan bracket. We also study the unital simple Jordan superalgebras whose even part is a field. We demonstrate that each of these superalgebras is either a superalgebra of a nondegenerate bilinear form, or a four-dimensional simple Jordan superalgebra, or a superalgebra of a Jordan bracket, or a superalgebra whose odd part is an irreducible module over a field.
Keywords:associative commutative superalgebra, Jordan superalgebra, differential algebra, Grassmann algebra, superalgebra of a bilinear form, derivation, composition algebra, superalgebra of a Jordan bracket, bracket of vector type, Poisson bracket, Kantor double.
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