Racks and Orbits of Dressing Transformations
A. Balinsky
TL;DR
This paper introduces a new algebraic structure on the orbits of dressing transformations in quasitriangular Poisson Lie groups, linking it to topological invariants and quantum field theories.
Contribution
It provides a novel algebraic framework for dressing transformation orbits and connects them to topological invariants and quantum field theory applications.
Findings
New algebraic structure on dressing transformation orbits
Topological interpretation of link invariants
Applications to 3D topological quantum field theories
Abstract
New algebraic structure on the orbits of dressing transformations of the quasitriangular Poisson Lie groups is provided. This give 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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology