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Zbl 0981.53079
Khimshiashvili, G.; Przybysz, R.
On generalized Sklyanin algebras. (English)
[J] Georgian Math. J. 7, No.4, 689-700 (2000). ISSN 1072-947X; ISSN 1572-9176/e

Summary: A class of algebraic Poisson structures on $\bbfR^4$ is introduced which contains the well-known Sklyanin algebras. For this class, an effective algebraic method of computing Euler characteristics of Casimir levels is developed which enables us to compute them in the case of Sklyanin algebras. It is also shown that one may associate a finite graph with every generalized Sklyanin algebra. Some related results and open problems are also presented.

MSC 2000:: *53D17 Poisson manifolds
57R20 Characteristic classes and numbers
58K65 Topological invariants

Keywords: Petrovsky number; algebraic Poisson structures; Sklyanin algebras; Euler characteristics; Casimir levels

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Zentralblatt MATH Berlin [Germany]