Simple 5-Dimensional Right Alternative Superalgebras with Trivial Even Part
- Authors: Pchelintsev S.V.1,2, Shashkov O.V.1
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Affiliations:
- Financial University Under the Government of the Russian Federation
- Sobolev Institute of Mathematics
- Issue: Vol 58, No 6 (2017)
- Pages: 1078-1089
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171607
- DOI: https://doi.org/10.1134/S0037446617060179
- ID: 171607
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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.
About the authors
S. V. Pchelintsev
Financial University Under the Government of the Russian Federation; Sobolev Institute of Mathematics
Author for correspondence.
Email: pchelinzev@mail.ru
Russian Federation, Moscow; Novosibirsk
O. V. Shashkov
Financial University Under the Government of the Russian Federation
Email: pchelinzev@mail.ru
Russian Federation, Moscow