@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}, pages = {15--34}, publisher = {Gauthier-Villars}, volume = {53}, number = {1}, year = {1990}, mrnumber = {1077464}, zbl = {0706.58012}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1990__53_1_15_0/} }
TY - JOUR AU - Beggs, Edwin AU - Majid, Shahn TI - Matched pairs of topological Lie algebras corresponding to Lie bialgebra structures on $diff(S^1)$ and $diff(\mathbf {R})$ JO - Annales de l'I.H.P. Physique théorique PY - 1990 SP - 15 EP - 34 VL - 53 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1990__53_1_15_0/ LA - en ID - AIHPA_1990__53_1_15_0 ER -
%0 Journal Article %A Beggs, Edwin %A Majid, Shahn %T Matched pairs of topological Lie algebras corresponding to Lie bialgebra structures on $diff(S^1)$ and $diff(\mathbf {R})$ %J Annales de l'I.H.P. Physique théorique %D 1990 %P 15-34 %V 53 %N 1 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPA_1990__53_1_15_0/ %G en %F 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 53 (1990) no. 1, pp. 15-34. http://www.numdam.org/item/AIHPA_1990__53_1_15_0/
[AK] 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
and ,[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 | Zbl
,[Hil] A Course in Homological Algebra, Springer-Verlag, 1980.
and ,[KM] Poisson-Lie Groups and Complete Integrability, I, Ann. Inst. Henri-Poincaré, Ser. A, Vol. 49, 1988, pp. 433-460. | Numdam | MR | Zbl
and ,[Lu W] Poisson Lie Groups, Dressing Transformations and Bruhat Decompositions, J. Diff. Geom., Vol. 31, 1990, pp. 501-526. | MR | Zbl
and ,[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 | Zbl
,[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 | Zbl
,[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 | Zbl
,Hopf Algebras for Physics at the Planck Scale J. Class. Quantum Gravity, Vol. 5, 1988, pp. 1587-1606. | MR | Zbl
,[Mack] Products of Subgroups and Projective Multipliers, Colloq. Math. Soc. Janos Bolyais, Vol. 5, Hilbert Space Operators, Tihany, Hungary, 1970. | Zbl
,[Mic] Lie Coalgebras, Adv. Math., Vol. 38, 1980, pp. 1-54. | MR | Zbl
[Seg] Two Dimensional Conformal Field Theories and Modular Functors, in Proc. ICMP, Swansca, Adam Hilger, 1989, pp. 22-37. | MR
,[Sem] Dressing Transformations and Poisson Group Actions, Publ. R.I.M.S., Kyoto, Vol. 21, 1985, pp. 1237-1260. | MR | Zbl
,[Tak] Matched Pairs of Groups and Bismash Products of Hopf Algebras, Comm. Alg., Vol. 9, 1981, pp. 841-882. | MR | Zbl
,[Wit] Coadjoint Representations of the Virasoro Group, Comm. Math. Phys., Vol. 114, 1988, p. 1. | MR | Zbl
,[Yas] Initial Value Decomposition of the Spacetime Diffeomorphism Group, AMS JSR Conf. Math. GR, Santa Cruz, 1986. | MR | Zbl
,