Two results on a class of Poisson structures on Lie groups.
Luen-Chau Li (1992)
Mathematische Zeitschrift
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Luen-Chau Li (1992)
Mathematische Zeitschrift
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Vaisman, Izu (2000)
Journal of Lie Theory
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Jan Vysoký, Ladislav Hlavatý (2012)
Archivum Mathematicum
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Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle. The elegant form of equations of motion for so called Poisson-Lie groups is derived. Construction of the Poisson-Lie group corresponding to a given Lie bialgebra is widely known only for coboundary Lie bialgebras....
A. A. Balinsky (2000)
Commentationes Mathematicae Universitatis Carolinae
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A new algebraic structure on the orbits of dressing transformations of the quasitriangular Poisson Lie groups is provided. This gives the topological interpretation of the link invariants associated with the Weinstein-Xu classical solutions of the quantum Yang-Baxter equation. Some applications to the three-dimensional topological quantum field theories are discussed.
Nguyen Van Khue (1990)
Annales Polonici Mathematici
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Yvette Kosmann-Schwarzbach, Franco Magri (1990)
Annales de l'I.H.P. Physique théorique
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Veronique Chloup (2000)
Banach Center Publications
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The aim of this paper is to give an overview concerning the problem of linearization of Poisson structures, more precisely we give results concerning Poisson-Lie groups and we apply those cohomological techniques to star products.
Pietro Tortella (2012)
Open Mathematics
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Let X be a complex smooth projective variety, and G a locally free sheaf on X. We show that there is a one-to-one correspondence between pairs (Λ, Ξ), where Λ is a sheaf of almost polynomial filtered algebras over X satisfying Simpson’s axioms and is an isomorphism, and pairs (L, Σ), where L is a holomorphic Lie algebroid structure on and Σ is a class in F 1 H 2(L, ℂ), the first Hodge filtration piece of the second cohomology of L. As an application, we construct moduli spaces of...