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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 11, Pages 64–72
(Mi ivm9053)
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This article is cited in 2 scientific papers (total in 2 papers)
On minimal Poisson algebras
S. M. Ratseev Chair of Information Security and Control Theory, Ul'yanovsk State University, 42 L. Tolstoy str., Ul'yanovsk, 432017 Russia
Abstract:
We give Poisson algebra constructions on the base of associative algebras and we explore the relationship between the obtained Poisson algebras and original associative algebras. Based on the obtained structures we give two classes of minimal varieties of Poisson algebras of polynomial growth, i.e., the sequence of codimensions of any such a variety grows as a polynomial of some degree $k$, but the sequence of codimensions of any proper subvariety grows as a polynomial of degree strictly less than $k$. Previously the author showed that there are only two varieties of Poisson algebras of almost polynomial growth. In this paper we give a complete description of all subvarieties of these two varieties.
Keywords:
Poisson algebra, associative algebra, variety of algebras, growth of a variety.
Received: 26.03.2014
Citation:
S. M. Ratseev, “On minimal Poisson algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 11, 64–72; Russian Math. (Iz. VUZ), 59:11 (2015), 54–61
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https://www.mathnet.ru/eng/ivm9053 https://www.mathnet.ru/eng/ivm/y2015/i11/p64
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Abstract page: | 156 | Full-text PDF : | 42 | References: | 39 | First page: | 13 |
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