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This article is cited in 1 scientific paper (total in 1 paper)
Lie type Jordan algebras
A. V. Popov 19–144 Acad. Filatov ave., Ul'yanovsk, 432064 Russia
Abstract:
We study the variety $\mathcal{V}_J$ of Jordan algebras defined by the identities $x^2yx\equiv 0$ and $(x_1y_1)(x_2y_2)(x_3y_3)\equiv 0$. We suggest a method for constructing an algebra in $\mathcal{V}_J$ from an arbitrary Lie superalgebra. For certain subvarieties, we completely describe their identities and sequences of cocharacters. As a corollary, we obtain the first example of a variety of Jordan algebras with fractional exponential growth.
Key words:
solvable Lie algebras, polynomial identities, sequence of cocharacters of a variety, growth of varieties of algebras, fractional exponential growth.
Received: 05.01.2018 Revised: 05.08.2018 Accepted: 10.10.2018
Citation:
A. V. Popov, “Lie type Jordan algebras”, Mat. Tr., 22:1 (2019), 127–177; Siberian Adv. Math., 29:4 (2019), 274–307
Linking options:
https://www.mathnet.ru/eng/mt351 https://www.mathnet.ru/eng/mt/v22/i1/p127
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Abstract page: | 506 | Full-text PDF : | 89 | References: | 52 | First page: | 13 |
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