A basis for the Birman-Wenzl algebra

Details A basis for the Birman-Wenzl algebra A basis for the Birman-Wenzl algebra

2010-12-14

arxiv.org/abs/1012.3116v1

Mathematics

Quantum Algebra

This is a lightly edited version of an article written in 1989 but never fully completed. It was originally intended as a join

Scientific paper

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.

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