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This article is cited in 9 scientific papers (total in 9 papers)
Correlation of Poisson Algebras and Lie Algebras in the Language of Identities
S. M. Ratseev Ulyanovsk State University
Abstract:
In the paper, the varieties of Poisson algebras whose ideals of identities contain the identity $\{x,y\}\cdot\{z,t\}=0$ are studied, and the correlation of these varieties with varieties of Lie algebras is investigated. A variety of Poisson algebras of almost exponential growth is presented. An example of a variety of Poisson algebras with fractional exponent is also given.
Keywords:
Poisson algebra, Lie algebra, ideal of identities, variety of algebras, almost exponential growth, Specht variety.
Received: 26.12.2012 Revised: 26.06.2013
Citation:
S. M. Ratseev, “Correlation of Poisson Algebras and Lie Algebras in the Language of Identities”, Mat. Zametki, 96:4 (2014), 567–577; Math. Notes, 96:4 (2014), 538–547
Linking options:
https://www.mathnet.ru/eng/mzm10252https://doi.org/10.4213/mzm10252 https://www.mathnet.ru/eng/mzm/v96/i4/p567
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Abstract page: | 380 | Full-text PDF : | 170 | References: | 50 | First page: | 28 |
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