Abstract
Simple nonassociative alternative superalgebras are classified. Any such superalgebra either is trivial (i.e., has zero odd part) or has characteristic 2 or 3 and is isomorphic over its center to a superalgebra of one of the following five types: in characteristic 3, these are two superalgebras of dimensions 3 and 6 and a “twisted superalgebra of vector type,” which either is infinite-dimensional or has dimension 2·3n; in characteristic 2, those are either a Cayley-Dixon algebra with a grading induced by the Cayley-Dixon process or a “double Cayley-Dixon algebra.” Under certain constraints on the structure of even parts, we also give a description of prime nonassociative alternative nontrivial superalgebras in terms of central orders of simple superalgebras. The simple superalgebras of dimensions 3 and 6 are then used to construct simple Jordan superalgebras of characteristic 3 and of dimensions 12 and 21, respectively.
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Additional information
Supported by the FICYT (Asturias, Spain), and by RFFR grant No. 96-01-01511.
Translated fromAlgebra i Logika, Vol. 36, No. 6, pp. 675–716, November–December, 1997.
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Shestakov, I.P. Prime alternative superalgebras of arbitrary characteristic. Algebr Logic 36, 389–412 (1997). https://doi.org/10.1007/BF02671556
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DOI: https://doi.org/10.1007/BF02671556