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On generalized Sklyanin algebras. (English) Zbl 0981.53079
Summary: A class of algebraic Poisson structures on 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:
53D17Poisson manifolds; Poisson groupoids and algebroids
57R20Characteristic classes and numbers (differential topology)
58K65Topological invariants (singularities, catastrophe theory)