@article{AIHPA_1990__53_1_15_0,
author = {Beggs, Edwin and Majid, Shahn},
title = {Matched pairs of topological Lie algebras corresponding to Lie bialgebra structures on $diff(S^1)$ and $diff(\mathbf {R})$},
journal = {Annales de l'I.H.P. Physique th\'eorique},
volume = {52},
year = {1990},
pages = {15-34},
mrnumber = {1077464},
zbl = {0706.58012},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPA_1990__53_1_15_0}
}
Beggs, Edwin; Majid, Shahn. Matched pairs of topological Lie algebras corresponding to Lie bialgebra structures on $diff(S^1)$ and $diff(\mathbf {R})$. Annales de l'I.H.P. Physique théorique, Tome 52 (1990) pp. 15-34. http://gdmltest.u-ga.fr/item/AIHPA_1990__53_1_15_0/
[AK] and , Bigèbres de Lie, Doubles et Carrés, Ann. Inst. Henri-Poincaré, Vol. 49, (4), 1988, pp. 461-478; , Bigèbres de Lie, Structures de Poisson et Variantes de l'équation de Yang-Baxter, Publ. I.R.M.A., Univ. Lille, Vol. 9, (3), 1987; , Groupes de Lie-Poisson et Bigèbres de Lie, Univ. Lille PhD Thesis, 1988. | Numdam | Zbl 0667.16006
[Bak] , Gelfand-Dickey Algebras and Higher Spin Fields, preprint, 1988.
[Dri] , Hamiltonian Structures on Lie Groups, Lie Bialgebras and the Geometric Meaning of the Classical Yang-Baxter Equations, Sov. Math. Dokl., Vol. 27, 1983, p. 68. | MR 688240 | Zbl 0526.58017
[Hil] and , A Course in Homological Algebra, Springer-Verlag, 1980.
[KM] and , Poisson-Lie Groups and Complete Integrability, I, Ann. Inst. Henri-Poincaré, Ser. A, Vol. 49, 1988, pp. 433-460. | Numdam | MR 988946 | Zbl 0667.16005
[Lu W] and , Poisson Lie Groups, Dressing Transformations and Bruhat Decompositions, J. Diff. Geom., Vol. 31, 1990, pp. 501-526. | MR 1037412 | Zbl 0673.58018
[M 1] , Physics for Algebraists: Non-commutative and Non-cocommutative Hopf Algebras by a Bicrossproduct Construction, in Harvard Ph D Thesis, 1988 and J. algebra, Vol. 130, 1990, pp. 17-64. | MR 1045735 | Zbl 0694.16008
[M 2] , Matched Pairs of Lie Groups Associated to Solutions of the Classical Yang-Baxter Equations, in Harvard PhD Thesis, 1988 and Pac. J. Math., Vol. 141, 1990, pp. 311-332. | MR 1035446 | Zbl 0735.17017
[M 3] , Matched Pairs of Lie Groups and Hopf Algebra Bicrossproducts, Nucl. Phys. B, Proc. Supl., Vol. 6, 1989, pp. 422-424; , Hopf von Neumann Algebra Bicrossproducts, Kac Algebra Bicrossproducts, and the Classical Yang-Baxter Equations in Harvard Ph D Thesis (1988) and to appear J. Funct. Anal.; | MR 1126075 | Zbl 0959.16500
, Hopf Algebras for Physics at the Planck Scale J. Class. Quantum Gravity, Vol. 5, 1988, pp. 1587-1606. | MR 973262 | Zbl 0672.16009
[Mack] , Products of Subgroups and Projective Multipliers, Colloq. Math. Soc. Janos Bolyais, Vol. 5, Hilbert Space Operators, Tihany, Hungary, 1970. | Zbl 0251.22005
[Mic] Lie Coalgebras, Adv. Math., Vol. 38, 1980, pp. 1-54. | MR 594993 | Zbl 0451.16006
[Seg] , Two Dimensional Conformal Field Theories and Modular Functors, in Proc. ICMP, Swansca, Adam Hilger, 1989, pp. 22-37. | MR 1033753
[Sem] , Dressing Transformations and Poisson Group Actions, Publ. R.I.M.S., Kyoto, Vol. 21, 1985, pp. 1237-1260. | MR 842417 | Zbl 0674.58038
[Tak] , Matched Pairs of Groups and Bismash Products of Hopf Algebras, Comm. Alg., Vol. 9, 1981, pp. 841-882. | MR 611561 | Zbl 0456.16011
[Wit] , Coadjoint Representations of the Virasoro Group, Comm. Math. Phys., Vol. 114, 1988, p. 1. | MR 925520 | Zbl 0632.22015
[Yas] , Initial Value Decomposition of the Spacetime Diffeomorphism Group, AMS JSR Conf. Math. GR, Santa Cruz, 1986. | MR 954425 | Zbl 0647.58011