Transactions of the American Mathematical Society

Author(s): S. P. Mishchenko; V. M. Petrogradsky; A. Regev
Journal: Trans. Amer. Math. Soc. 359 (2007), 4669-4694.
MSC (2000): Primary 17B63, 17B01, 16P90, 16R10
Posted: May 1, 2007
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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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S. P. Mishchenko
Affiliation: Faculty of Mathematics, Ulyanovsk State University, Leo Tolstoy 42, Ulyanovsk, 432970 Russia
Email: mishchenkosp@mail.ru, mishchenkosp@ulsu.ru

V. M. Petrogradsky
Affiliation: Faculty of Mathematics, Ulyanovsk State University, Leo Tolstoy 42, Ulyanovsk, 432970 Russia
Email: petrogradsky@hotbox.ru

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