### Far Eastern Mathematical Journal

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On minimal Leibniz – Poisson algebras of polynomial growth

S. M. Ratseev

2014, issue 2, Ñ. 248–256

Abstract
Let $\{\gamma_n({\mathbf V})\}_{n\geq 1}$ be the sequence of proper codimension growth of a variety of Leibniz – Poisson algebras ${\mathbf V}$. We give one class of minimal varieties of Leibniz – Poisson algebras of polynomial growth of the sequence $\{\gamma_n({\mathbf V})\}_{n\geq 1}$, i.e. the sequence of proper codimensions of any such variety grows as a polynomial of some degree $k$, but the sequence of proper codimensions of any proper subvariety grows as a polynomial of degree strictly less than $k$.

Keywords:
Poisson algebra, Leibniz – Poisson algebra, variety of algebras, growth of a variety