Poisson PI algebras

Mishchenko, S.; Petrogradsky, V.; Regev, A.

doi:10.1090/S0002-9947-07-04008-1

Poisson PI algebras
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by S. P. Mishchenko, V. M. Petrogradsky and A. Regev PDF

Trans. Amer. Math. Soc. 359 (2007), 4669-4694 Request permission

Abstract:

We study Poisson algebras satisfying polynomial identities. In particular, such algebras satisfy “customary” identities (Farkas, 1998, 1999) Our main result is that the growth of the corresponding codimensions of a Poisson algebra with a nontrivial identity is exponential, with an integer exponent. We apply this result to prove that the tensor product of Poisson PI algebras is a PI-algebra. We also determine the growth of the Poisson-Grassmann algebra and of the Hamiltonian algebras $\mathbf {H}_{2k}$.

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