|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
20 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Affine Birman-Wenzl-Murakami Algebras and Tangles in the Solid Torus | | Frederick M. Goodman
; Holly M. Hauschild
; | | Date: |
7 Nov 2004 | | Subject: | Quantum Algebra; Geometric Topology; Representation Theory MSC-class: 57M25, 17B37 | math.QA math.GT math.RT | | Abstract: | The ordinary (or classical) Birman-Wenzl-Murakami algebras were initially conceived as an algebraic framework for the Kauffman link invariant. They also appear as centralizer algebras for representations of quantum universal enveloping algebras of orthogonal or symplectic types. It was shown by Morton and Wassermann that the BMW algebras are isomorphic to algebras of tangles in (disc $ imes$ interval), modulo Kauffman skein relations. This isomorphism allows one to see very clearly certain properties of the BMW algebras -- for example existence of Markov traces and conditional expectations and a good basis. In the present work, we establish the correponding results for affine BMW algebras, showing they are isomorphic to algebras of tangles in (annulus $ imes$ interval), modulo Kaufffman skein relations. Again, this provides an important foundation for studying these algebras, as the existence of Markov traces and conditional expectations are consequences of the isomorphism. Moreover, we obtain a basis of the affine BMW algebras analogous to a well known basis of the affine Hecke algebras. | | Source: | arXiv, math.QA/0411155 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER