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.Comment: 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 figure
