, Volume 36, Issue 6, pp 389412
Prime alternative superalgebras of arbitrary characteristic
 I. P. Shestakov
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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 infinitedimensional or has dimension 2·3^{n}; in characteristic 2, those are either a CayleyDixon algebra with a grading induced by the CayleyDixon process or a “double CayleyDixon 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.
 Title
 Prime alternative superalgebras of arbitrary characteristic
 Journal

Algebra and Logic
Volume 36, Issue 6 , pp 389412
 Cover Date
 199711
 DOI
 10.1007/BF02671556
 Print ISSN
 00025232
 Online ISSN
 15738302
 Publisher
 Kluwer Academic PublishersPlenum Publishers
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