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Poisson (co)homology of polynomial Poisson algebras in dimension four: Sklyanin’s case. (English) Zbl 1173.53332
Summary: We compute the Poisson (co)homology of a polynomial Poisson structure given by two Casimir polynomial functions which define a complete intersection with an isolated singularity.
53D17Poisson manifolds; Poisson groupoids and algebroids
14F43Other algebro-geometric (co)homologies
[1]Artin, Michael; Schelter, William F.: Graded algebras of global dimension 3, Adv. math. 66, No. 2, 171-216 (1987) · Zbl 0633.16001 · doi:10.1016/0001-8708(87)90034-X
[2]Boos, H.; Jimbo, M.; Miwa, T.; Smirnov, F.; Takeyama, Y.: Traces on the Sklyanin algebra and correlation functions of the eight-vertex model, J. phys. A 38, No. 35, 7629-7659 (2005) · Zbl 1082.81043 · doi:10.1088/0305-4470/38/35/003
[3]Brylinski, Jean-Luc: A differential complex for Poisson manifolds, J. differential geom. 28, No. 1, 93-114 (1988) · Zbl 0634.58029 · doi:euclid:jdg/1214442161
[4]Drinfel’d, V. G.: Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of classical Yang – Baxter equations, Dokl. akad. Nauk SSSR 268, No. 2, 285-287 (1983) · Zbl 0526.58017
[5]Ginzburg, Viktor L.; Weinstein, Alan: Lie – Poisson structure on some Poisson Lie groups, J. amer. Math. soc. 5, No. 2, 445-453 (1992) · Zbl 0766.58018 · doi:10.2307/2152773
[6]Khimshiashvili, G.: On one class of exact Poisson structures, Proc. A. Razmadze math. Inst. 119, 111-120 (1999) · Zbl 1060.53502
[7]Khimshiashvili, G.; Przybysz, R.: On generalized Sklyanin algebras, Georgian math. J. 7, No. 4, 689-700 (2000) · Zbl 0981.53079
[8]Lichnerowicz, André: LES variétés de Poisson et leurs algèbres de Lie associées, J. differential geom. 12, No. 2, 253-300 (1977) · Zbl 0405.53024
[9]Looijenga, E. J. N.: Isolated singular points on complete intersections, London math. Soc. lecture note ser. 77 (1984) · Zbl 0552.14002
[10]Marconnet, Nicolas: Homologies of cubic Artin – Schelter regular algebras, J. algebra 278, No. 2, 638-665 (2004) · Zbl 1067.53064 · doi:10.1016/j.jalgebra.2003.11.019
[11]Odesskiĭ, A. V.; Rubtsov, V. N.: Polynomial Poisson algebras with a regular structure of symplectic leaves, Teoret. mat. Fiz. 133, No. 1, 3-23 (2002) · Zbl 1138.53314 · doi:10.1023/A:1020673412423
[12]Pichereau, Anne: Poisson (co)homology and isolated singularities, J. algebra 299, No. 2, 747-777 (2006) · Zbl 1113.17009 · doi:10.1016/j.jalgebra.2005.10.029
[13]Saito, Kyoji: On a generalization of de-Rham lemma, Ann. inst. Fourier (Grenoble) 26, No. 2, 165-170 (1976) · Zbl 0338.13009 · doi:10.5802/aif.620 · doi:numdam:AIF_1976__26_2_165_0
[14]Sklyanin, E. K.: Some algebraic structures connected with the Yang – Baxter equation, Funktsional. anal. I prilozhen. 16, No. 4, 27-34 (1982) · Zbl 0513.58028 · doi:10.1007/BF01077848
[15]Sklyanin, E. K.: Some algebraic structures connected with the Yang – Baxter equation. Representations of a quantum algebra, Funktsional. anal. I prilozhen. 17, No. 4, 34-48 (1983) · Zbl 0536.58007 · doi:10.1007/BF01076718
[16]Pelap, Serge Roméo Tagne: On the hochshild homology of elliptic Sklyanin algebra, Lett. math. Phys. 87, 267-281 (2009) · Zbl 1176.16011 · doi:10.1007/s11005-009-0307-6
[17]Den Bergh, Michel Van: Noncommutative homology of some three-dimensional quantum spaces, K-theory 8, 213-230 (1994) · Zbl 0814.16006 · doi:10.1007/BF00960862
[18]Weibel, Charles A.: An introduction to homological algebra, Cambridge stud. Adv. math. 38 (1994) · Zbl 0797.18001
[19]Xu, Ping: Gerstenhaber algebras and BV-algebras in Poisson geometry, Comm. math. Phys. 200, No. 3, 545-560 (1999) · Zbl 0941.17016 · doi:10.1007/s002200050540