On minimal Poisson algebras
type: Item
instance of: scholarly article
title: On minimal Poisson algebras
zbMATH Open document ID: 1359.17035
DOI: 10.3103/S1066369X15110067
author: N. E. Zubov
published in: Russian Mathematics
publication date: 2016-01-21T00:00:00Z
review text: The author constructs Poisson algebras starting with associative algebras. See a similar construction in the author's article [Math. Notes 96, No. 4, 538--547 (2014); translation from Mat. Zametki 96, No. 4, 567--577 (2014; Zbl 1359.17034)]. Using this construction, the author gives two classes of minimal varieties of Poisson algebras of polynomial growth, namely the codimension growth sequence of these varieties grows polynomially of degree \(k\), but the codimension sequence of any proper subvariety is a polynomial of smaller degree. Also, the author gives a complete description of all subvarieties of these two varieties.
Mathematics Subject Classification ID: 17B63
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 16P90
Mathematics Subject Classification ID: 17B60
zbMATH DE Number: 6534155
zbMATH Keywords: Poisson algebra
zbMATH Keywords: polynomial identity
zbMATH Keywords: variety of algebras
zbMATH Keywords: codimension growth
zbMATH Keywords: polynomial growth
reviewed by: Victor Petrogradsky
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6534155