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Journal of Siberian Federal University. Mathematics & Physics, 2013, Volume 6, Issue 1, Pages 97–104
(Mi jsfu293)
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This article is cited in 5 scientific papers (total in 5 papers)
On varieties of Leibniz–Poisson algebras with the identity {x,y}⋅{z,t}=0
Sergey M. Ratseev Department of Mathematics and Information Technologies, Ulyanovsk State University, Ulyanovsk, Russia
Abstract:
Let K be an arbitrary field and let A be a K-algebra. The polynomial identities satisfied by A can be measured through the asymptotic behavior of the sequence of codimensions of A. We study varieties of Leibniz–Poisson algebras, whose ideals of identities contain the identity {x,y}⋅{z,t}=0, we study an interrelation between such varieties and varieties of Leibniz algebras. We show that from any Leibniz algebra L one can construct the Leibniz–Poisson algebra A and the properties of L are close to the properties of A. We show that if the ideal of identities of a Leibniz–Poisson variety V does not contain any Leibniz polynomial identity then V has overexponential growth of the codimensions. We construct a variety of Leibniz–Poisson algebras with almost exponential growth.
Keywords:
Poisson algebra, Leibniz–Poisson algebra, variety of algebras, growth of a variety.
Received: 12.11.2012 Received in revised form: 12.11.2012 Accepted: 15.11.2012
Citation:
Sergey M. Ratseev, “On varieties of Leibniz–Poisson algebras with the identity {x,y}⋅{z,t}=0”, J. Sib. Fed. Univ. Math. Phys., 6:1 (2013), 97–104
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https://www.mathnet.ru/eng/jsfu293 https://www.mathnet.ru/eng/jsfu/v6/i1/p97
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