## 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 $\mathbf {H}_{2k}$.## References

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## Additional Information

**S. P. Mishchenko**- Affiliation: Faculty of Mathematics, Ulyanovsk State University, Leo Tolstoy 42, Ulyanovsk, 432970 Russia
- MR Author ID: 189236
- 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
- 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
- © Copyright 2007 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**359**(2007), 4669-4694 - MSC (2000): Primary 17B63, 17B01, 16P90, 16R10
- DOI: https://doi.org/10.1090/S0002-9947-07-04008-1
- MathSciNet review: 2320646