(Quasi-)Poisson enveloping algebras

Preprint English OPEN
Yang, Yan-Hong; Yao, Yuan; Ye, Yu;
(2010)
  • Subject: Mathematics - Category Theory | Mathematics - Rings and Algebras | 16S40, 17B63
    arxiv: Mathematics::Category Theory | Astrophysics::Solar and Stellar Astrophysics

We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quas... View more
  • References (17)
    17 references, page 1 of 2

    [1] Y.H. Bao and Y. Ye, On quasi-Poisson cohomology, in preparation.

    [2] W. Crawley-Boevey, P. Etingof and V. Ginzburg, Noncommutative geometry and quiver algebras. Adv. Math. 209 (2007) 274-336.

    [3] J.M. Casas and T. Pirashvili, Algebras with bracket. Manuscripta Math. 119 (2006) 1-15.

    [4] D. Farkas, Modules for Poisson Algebras. Comm. in Algebra 28 (7) (2000) 3293-3306.

    [5] M. Flato, M. Gerstenhaber and A.A. Voronov, Cohomology and deformation of Leibniz pairs. Lett. Math. Phys. 34 (1995), 77-90.

    [6] D. Farkas and G. Letzter, Ring Theory from Symplectic Geometry. Journal of Pure and Applied Algebra 225(1998) 255-290.

    [7] V. Ginzburg and M. Kapranov, Koszul duality for operads. Duke Math. J. 76 (1) (1994) 203-272.

    [8] M. Kontsevich, Formal (non)commutative symplectic geometry. The Gelfand Math. Seminars, 1990-1992, Birkh¨auser, Boston, MA, 173-187.

    [9] F. Kubo, Finite-dimensional Simple Leibniz Pairs and Simple Poisson Modules. Lett. Math.Phys. 43 (1) (1998) 21-29.

    [10] F. Loose, Symplectic algebras and Poisson algebras. Commun. Algebras 21 (7) (1993) 2395-2416.

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