A basis for the Birman-Wenzl algebra


Morton, HR ORCID: 0000-0002-8524-2695 (2010) A basis for the Birman-Wenzl algebra. ArXiv. (Unpublished)

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Abstract

An explicit isomorphism is constructed between the Birman-Wenzl algebra, defined algebraically by J. Birman and H. Wenzl using generators and relations, and the Kauffman algebra, constructed geometrically by H. R. Morton and P. Traczyk in terms of tangles. The isomorphism is obtained by constructing an explicit basis in the Birman-Wenzl algebra, analogous to a basis previously constructed for the Kauffman algebra using 'Brauer connectors'. The geometric isotopy arguments for the Kauffman algebra are systematically replaced by algebraic versions using the Birman-Wenzl relations.

Item Type: Article
Additional Information: This is a lightly edited version of an article written in 1989 but never fully completed. It was originally intended as a joint paper with A. J.Wassermann. 33 pages, 20 figures
Uncontrolled Keywords: math.QA, math.QA, math.RT, 57M25
Subjects: ?? QA ??
Divisions: Faculty of Science and Engineering > School of Physical Sciences > Mathematical Sciences
Depositing User: Symplectic Admin
Date Deposited: 23 Dec 2011 15:45
Last Modified: 17 Dec 2022 01:28
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/1477
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