Cite this article as:
Ratseev S. M. On Poisson Customary Polynomial Identities. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 2, pp. 150-155. DOI: https://doi.org/10.18500/1816-9791-2014-14-2-150-155
Language:
Russian
Heading:
UDC:
512.572
On Poisson Customary Polynomial Identities
Abstract:
We study Poisson customary and Poisson extended customary polynomials. We show that the sequence of codimensions {rn(V )}n¸1 of every extended customary space of variety V of Poisson algebras over an arbitrary field is either bounded by a polynomial or at least exponential. Furthermore, if this sequence is bounded by polynomial then there is a polynomial R(x) with rational coefficients such that rn(V ) = R(n) for all sufficiently large n. We present lower and upper bounds for the polynomials R(x) of an arbitrary fixed degree.
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References
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