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math-ph2012★ 4 cited
Confluence on the Painlevé Monodromy Manifolds, their Poisson Structure and Quantisation
Marta Mazzocco, Vladimir Rubtsov
In this paper we obtain a system of flat coordinates on the monodromy manifold of each of the Painlevé equations. This allows us to quantise such manifolds. We produce a quantum co…
math.QA2012
Algebraic properties of Manin matrices II: q-analogues and integrable systems
A. Chervov, G. Falqui, V. Rubtsov +1
We study a natural q-analogue of a class of matrices with noncommutative entries, which were first considered by Yu. I. Manin in 1988 in relation with quantum group theory, (called…
nlin.SI2012
Double Poisson brackets on free associative algebras
A. Odesskii, V. Rubtsov, V. Sokolov
We discuss double Poisson structures in sense of M. Van den Bergh on free associative algebras focusing on the case of quadratic Poisson brackets. We establish their relations with…