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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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