Racks and orbits of dressing transformations

A. A. Balinsky

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 3, page 437-444
  • ISSN: 0010-2628

Abstract

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A new algebraic structure on the orbits of dressing transformations of the quasitriangular Poisson Lie groups is provided. This gives the topological interpretation of the link invariants associated with the Weinstein-Xu classical solutions of the quantum Yang-Baxter equation. Some applications to the three-dimensional topological quantum field theories are discussed.

How to cite

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Balinsky, A. A.. "Racks and orbits of dressing transformations." Commentationes Mathematicae Universitatis Carolinae 41.3 (2000): 437-444. <http://eudml.org/doc/248604>.

@article{Balinsky2000,
abstract = {A new algebraic structure on the orbits of dressing transformations of the quasitriangular Poisson Lie groups is provided. This gives the topological interpretation of the link invariants associated with the Weinstein-Xu classical solutions of the quantum Yang-Baxter equation. Some applications to the three-dimensional topological quantum field theories are discussed.},
author = {Balinsky, A. A.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {automorphic set; Poisson Lie group; link invariants; automorphic set; Poisson Lie group; link invariants},
language = {eng},
number = {3},
pages = {437-444},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Racks and orbits of dressing transformations},
url = {http://eudml.org/doc/248604},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Balinsky, A. A.
TI - Racks and orbits of dressing transformations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 3
SP - 437
EP - 444
AB - A new algebraic structure on the orbits of dressing transformations of the quasitriangular Poisson Lie groups is provided. This gives the topological interpretation of the link invariants associated with the Weinstein-Xu classical solutions of the quantum Yang-Baxter equation. Some applications to the three-dimensional topological quantum field theories are discussed.
LA - eng
KW - automorphic set; Poisson Lie group; link invariants; automorphic set; Poisson Lie group; link invariants
UR - http://eudml.org/doc/248604
ER -

References

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  9. Balinsky A., Braid Groups, in ``Oper. Theor. in Funct. Spaces'', ed. E. Gordon and M. Antonetz, Gorki State Univ., 1991 (in Russian). 
  10. Balinsky A., Weinstein-Xu invariants and link group representations I, e-preprint hep-th/9404168. 
  11. Birman J.S., New points of view in knot theory, Bull. Amer. Math. Soc. 28 253-287 (1993). (1993) Zbl0785.57001MR1191478
  12. Jones V.F.R., A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 103-111 (1985). (1985) Zbl0564.57006MR0766964
  13. Drinfeld V.G., On some unsolved problems in quantum group theory, Lecture Notes in Math. 1510, 1992, pp.1-8. Zbl0765.17014MR1183474
  14. Freyd P.J., Yetter D.N., Braided compact closed categories with applications to low-dimensional topology, Adv. in Math. 77 (2) 156-182 (1989). (1989) Zbl0679.57003MR1020583
  15. Drinfeld V.G., Hamiltonian structures on Lie groups, Lie bialgebras and geometrical meaning of classical Yang-Baxter equations, Dokl. Akad. Nauk SSSR 2 285-287 (1982). (1982) MR0688240
  16. Reshetikhin N., Semenov-Tian-Shansky M., Quantum R-matrices and factorization problems, J. Diff. Geom. 31 533-550 (1988). (1988) Zbl0711.17008MR1075721
  17. Semenov-Tian-Shansky M.A., Dressing transformations and Poisson Lie group actions, Publ. RIMS, Kyoto University 21 1237-1260 (1985). (1985) MR0842417
  18. Weinstein A., Some remarks on dressing transformations, J. Fac. Sci. Univ. Tokyo, Sect. A, Math. 36 163-167 (1988). (1988) Zbl0653.58012MR0931446

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