Open AccessCOMMUTATIVE LEIBNIZ-POISSON ALGEBRAS OF POLYNOMIAL GROWTH
Author(s) -
С. М. Рацеев
Publication year - 2012
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2012-18-3.1-54-65
Subject(s) - commutative property , variety (cybernetics) , polynomial , mathematics , poisson distribution , pure mathematics , algebra over a field , mathematical analysis , statistics
In this paper we study commutative Leibniz-Poisson algebras. We prove that a variety of commutative Leibniz-Poisson algebras has either polynomial growth or growth with exponential not less than 2, the eld being arbitrary. We prove that every variety of commutative Leibniz-Poisson algebras of polynomial growth over a eld of characteristic 0 has a nite basis for its polynomial identities. Also we construct a variety of commutative Leibniz-Poisson algebras with almost polynomial growth.