Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-02-09
J.Math.Phys. 35 (1994) 5288-5305
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, 10 figures
Scientific paper
10.1063/1.530751
The correspondence of the braid group on a handlebody of arbitrary genus to the algebra of Yang-Baxter and extended reflection equation operators is shown. Representations of the infinite dimensional extended reflection equation algebra in terms of direct products of quantum algebra generators are derived, they lead to a representation of this braid group in terms of $R$-matrices. Restriction to the reflection equation operators only gives the coloured braid group. The reflection equation operators, describing the effect of handles attached to a 3-ball, satisfy characteristic equations which give rise to additional skein relations and thereby invariants of links on handlebodies. The origin of the skein relations is explained and they are derived from an adequately adapted handlebody version of the Jones polynomial. Relevance of these results to the construction of link polynomials on closed 3-manifolds via Heegard splitting and surgery is indicated.
No associations
LandOfFree
Extended reflection equation algebras, the braid group on a handlebody and associated link polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Extended reflection equation algebras, the braid group on a handlebody and associated link polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extended reflection equation algebras, the braid group on a handlebody and associated link polynomials will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-148702