Poisson PI algebras

• Autores: S. P. Mishchenko, V.M. Petrogradsky, Alon Regev
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 10, 2007, págs. 4669-4694
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04008-1
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• Resumen

  • 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.