In mathematics, a Lie bialgebra is the Lie-theoretic case of a bialgebra: it is a set with a Lie algebra and a Lie coalgebra structure which are compatible...
5 KB (953 words) - 01:25, 13 November 2023
In mathematics, a bialgebra over a field K is a vector space over K which is both a unital associative algebra and a counital coassociative coalgebra...
12 KB (1,612 words) - 10:08, 11 April 2024
counterpart of a Poisson–Lie group is a Lie bialgebra, in analogy to Lie algebras as the infinitesimal counterparts of Lie groups. Many quantum groups...
7 KB (1,124 words) - 02:39, 10 December 2023
algebra Index of a Lie algebra Lie algebra cohomology Lie algebra extension Lie algebra representation Lie bialgebra Lie coalgebra Lie operad Particle physics...
61 KB (10,457 words) - 02:56, 14 July 2024
Lie algebra Lie-* algebra Lie algebra bundle Lie algebra cohomology Lie algebra representation Lie algebroid Lie bialgebra Lie coalgebra Lie conformal algebra...
2 KB (252 words) - 05:29, 18 December 2022
Manin triple (category Lie algebras)
is a complex reductive Lie algebra. If (g, p, q) is a finite-dimensional Manin triple then p can be made into a Lie bialgebra by letting the cocommutator...
3 KB (354 words) - 04:27, 14 June 2020
vector bundles. Lie bialgebroids are the vector bundle version of Lie bialgebras. A Lie algebroid consists of a bilinear skew-symmetric operation [ ⋅ , ⋅...
8 KB (1,440 words) - 15:47, 18 August 2024
× V → F. Bialgebra: an associative algebra with a compatible coalgebra structure. Lie bialgebra: a Lie algebra with a compatible bialgebra structure...
18 KB (2,214 words) - 04:44, 10 January 2024
)} is a pre-Lie algebra. Lie coalgebra Lie bialgebra Lie algebra cohomology Frobenius algebra Quasi-Frobenius ring Jacobson, Nathan, Lie algebras, Republication...
2 KB (314 words) - 22:31, 19 June 2017
the Jacobi identity. Both this standard example and the double of a Lie bialgebra are special instances of Courant algebroids. A Courant algebroid consists...
8 KB (1,541 words) - 14:59, 18 August 2024