Results 21 to 30 of about 83 (77)
ON LIE BIALGEBRAS OF LOOPS ON ORIENTABLE SURFACES [PDF]
Journal of Knot Theory and Its Ramifications, 2008 Goldman [2] and Turaev [4] found a Lie bialgebra structure on the vector space generated by non-trivial free homotopy classes of loops on an orientable surface. Chas [1] by the aid of the computer, found a negative answer to Turaev's question about the characterization of the classes with cobracket zero as multiples of simple classes, in every surface
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Atiyah Classes of Lie Bialgebras
Journal of Lie Theory, 2019 The Atiyah class was originally introduced by M.F. Atiyah. It has many developments in recent years. One important case is the Atiyah classes of Lie algebra pairs. In this paper, we study the Atiyah class of the Lie algebra pair associated with a Lie bialgebra $(g,g^*)$.
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LIE BIALGEBRAS ARISING FROM POISSON BIALGEBRAS [PDF]
Journal of the Korean Mathematical Society, 2010 It gives a method to obtain a natural Lie bialgebra from a Poisson bialgebra by an algebraic point of view. Let g be a coboundary Lie bialgebra associated to a Poission Lie group G. As an application, we obtain a Lie bialgebra from a sub-Poisson bialgebra of the restricted dual of the universal enveloping algebra U(g).
Sei-Qwon Oh, Eun-Hee Cho
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Infinite-dimensional Lie bialgebras via affinization of perm bialgebras and pre-Lie bialgebras
Journal of AlgebraIt is known that the operads of perm algebras and pre-Lie algebras are the Koszul dual each other and hence there is a Lie algebra structure on the tensor product of a perm algebra and a pre-Lie algebra. Conversely, we construct a special perm algebra structure and a special pre-Lie algebra structure on the vector space of Laurent polynomials such that
Yuanchang Lin, Peng Zhou, Chengming Bai
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Generalized Lie bialgebras and Jacobi structures on Lie groups [PDF]
Israel Journal of Mathematics, 2003 We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal invariants of Lie groups endowed with a certain type of Jacobi structures.
Iglesias, David, Marrero, Juan C.
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Nijenhuis BiHom-Lie bialgebras and differential Lie bialgebras
Comments are welcome!
Liu, Jiaqi, Gao, Lin, Zhang, Yuanyuan
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Poisson-Lie T-Duality¶for Quasitriangular Lie Bialgebras
Communications in Mathematical Physics, 2001 42 pages Latex, no ...
Beggs, E. J., Majid, Shahn
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Multiplier Infinitesimal Bialgebras and Derivator Lie Bialgebras
, 2011 11 ...
Arango, Jesus Alonso Ochoa +2 more
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Extensions of Hopf Algebras and Lie Bialgebras [PDF]
Transactions of the American Mathematical Society, 2000 Let f \mathfrak {f} ,
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