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Poisson identities of enveloping algebras |
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| Authors: | A. Giambruno V. M. Petrogradsky |
| Affiliation: | (1) Dipartimento di Matematica ed Applicazioni, Universitá di Palermo, Via Archirafi 34, I-90123 Palermo, Italy;(2) Faculty of Mathematics, Ulyanovsk State University, Leo Tolstoy 42, Ulyanovsk, 432970, Russia |
| Abstract: | Let L be a restricted Lie algebra. The symmetric algebra Sp(L) of the restricted enveloping algebra u(L) has the structure of a Poisson algebra. We give necessary and sufficient conditions on L in order for the symmetric algebra Sp(L) to satisfy a multilinear Poisson identity. We also settle the same problem for the symmetric algebra S(L) of a Lie algebra L over an arbitrary field. The first author was partially supported by MIUR of Italy. The second author was partially supported by Grant RFBR-04-01- 00739. Received: 31 October 2005 |
| Keywords: | 17B63 17B50 17B01 16R10 |
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