Matched pairs of topological Lie algebras corresponding to Lie bialgebra structures on diff(S 1 ) and diff(𝐑)
Annales de l'I.H.P. Physique théorique, Tome 53 (1990) no. 1, pp. 15-34. 
@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] R. Aminou and Y. Kosmann-Schwarzbach, Bigèbres de Lie, Doubles et Carrés, Ann. Inst. Henri-Poincaré, Vol. 49, (4), 1988, pp. 461-478; R. Aminou, 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; R. Aminou, Groupes de Lie-Poisson et Bigèbres de Lie, Univ. Lille PhD Thesis, 1988. | Numdam | Zbl

[Bak] I. Bakas, Gelfand-Dickey Algebras and Higher Spin Fields, preprint, 1988.

[Dri] V.G. Drinfeld, 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] P.J. Hilton and U.S. Stammbach, A Course in Homological Algebra, Springer-Verlag, 1980.

[KM] Y. Kosmann-Schwarzbach and F. Magri, Poisson-Lie Groups and Complete Integrability, I, Ann. Inst. Henri-Poincaré, Ser. A, Vol. 49, 1988, pp. 433-460. | Numdam | MR | Zbl

[Lu W] J.-H. Lu and A. Weinstein, Poisson Lie Groups, Dressing Transformations and Bruhat Decompositions, J. Diff. Geom., Vol. 31, 1990, pp. 501-526. | MR | Zbl

[M 1] S. Majid, 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] S. Majid, 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] S. Majid, Matched Pairs of Lie Groups and Hopf Algebra Bicrossproducts, Nucl. Phys. B, Proc. Supl., Vol. 6, 1989, pp. 422-424; S. Majid, 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

S. Majid, Hopf Algebras for Physics at the Planck Scale J. Class. Quantum Gravity, Vol. 5, 1988, pp. 1587-1606. | MR | Zbl

[Mack] G.W. Mackey, Products of Subgroups and Projective Multipliers, Colloq. Math. Soc. Janos Bolyais, Vol. 5, Hilbert Space Operators, Tihany, Hungary, 1970. | Zbl

[Mic] W. Michaelis Lie Coalgebras, Adv. Math., Vol. 38, 1980, pp. 1-54. | MR | Zbl

[Seg] G.B. Segal, Two Dimensional Conformal Field Theories and Modular Functors, in Proc. ICMP, Swansca, Adam Hilger, 1989, pp. 22-37. | MR

[Sem] M.A. Semenov-Tian-Shansky, Dressing Transformations and Poisson Group Actions, Publ. R.I.M.S., Kyoto, Vol. 21, 1985, pp. 1237-1260. | MR | Zbl

[Tak] M. Takeuchi, Matched Pairs of Groups and Bismash Products of Hopf Algebras, Comm. Alg., Vol. 9, 1981, pp. 841-882. | MR | Zbl

[Wit] E. Witten, Coadjoint Representations of the Virasoro Group, Comm. Math. Phys., Vol. 114, 1988, p. 1. | MR | Zbl

[Yas] P. Yasskin, Initial Value Decomposition of the Spacetime Diffeomorphism Group, AMS JSR Conf. Math. GR, Santa Cruz, 1986. | MR | Zbl