Abstract
This paper examines Kevin McCrimmon's proposed definition for a quadratic Jordan superalgebra meaningful over an arbitrary ring of scalars. Efim Zel'manov has proposed two conditions that such a definition should satisfy: first, all the simple, finite-dimensional, linear Jordan superalgebras of characteristic 0 in Kac' classification should have simple, quadratic Jordan superalgebra analogs, and second, these should be essentially all the simple, finite-dimensional, quadratic Jordan superalgebras of characteristic 0. Here we verify the first condition. Specifically we study the quadratic superalgebra analogues of full linear superalgebras, Hermitian superalgebras, Kaplansky's superalgebras, Kac's split 10-dimensional superalgebra, and superalgebras of quadratic forms with base point.
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