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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Poisson PI algebras


Authors: S. P. Mishchenko, V. M. Petrogradsky and A. Regev
Journal: Trans. Amer. Math. Soc. 359 (2007), 4669-4694
MSC (2000): Primary 17B63, 17B01, 16P90, 16R10
Published electronically: May 1, 2007
MathSciNet review: 2320646
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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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Additional Information

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

A. Regev
Affiliation: Department of Theoretical Mathematics, Weizmann Institute of Science, Rehovot, Israel
Email: regev@wisdom.weizmann.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04008-1
PII: S 0002-9947(07)04008-1
Received by editor(s): August 23, 2004
Received by editor(s) in revised form: February 22, 2005
Published electronically: May 1, 2007
Additional Notes: This research was partially supported by Grant RFBR-04-01-00739
Article copyright: © Copyright 2007 American Mathematical Society