zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.
MSC:
53D17Poisson manifolds; Poisson groupoids and algebroids
14F43Other algebro-geometric (co)homologies
References:
[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