On the Riemann-Lie algebras and Riemann-Poisson Lie groups.
Boucetta, Mohamed (2005)
Journal of Lie Theory
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Boucetta, Mohamed (2005)
Journal of Lie Theory
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Yvette Kosmann-Schwarzbach, Franco Magri (1990)
Annales de l'I.H.P. Physique théorique
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Mackenzie, K.C.H. (1998)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Kenny De Commer (2015)
Banach Center Publications
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On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures...
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.
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.