Abstract
We study the simple right alternative superalgebras whose even part is trivial; i.e., the even part has zero product. A simple right alternative superalgebra with the trivial even part is singular. The first example of a singular superalgebra was given in [1]. The least dimension of a singular superalgebra is 5. We prove that the singular 5-dimensional superalgebras are isomorphic if and only if suitable quadratic forms are equivalent. In particular, there exists a unique singular 5-dimensional superalgebra up to isomorphism over an algebraically closed field.
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Original Russian Text Copyright © 2017 Pchelintsev S.V. and Shashkov O.V.
Moscow; Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 6, pp. 1387–1400, November–December, 2017
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Pchelintsev, S.V., Shashkov, O.V. Simple 5-Dimensional Right Alternative Superalgebras with Trivial Even Part. Sib Math J 58, 1078–1089 (2017). https://doi.org/10.1134/S0037446617060179
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DOI: https://doi.org/10.1134/S0037446617060179