Siberian Mathematical Journal

, Volume 58, Issue 6, pp 1078–1089 | Cite as

Simple 5-Dimensional Right Alternative Superalgebras with Trivial Even Part

Article

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.

Keywords

simple superalgebra singular superalgebra right alternative superalgebra 

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Financial University Under the Government of the Russian FederationMoscowRussia
  2. 2.Sobolev Institute of MathematicsNovosibirskRussia

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