2010/12/14 by H. R. Morton, Morton, H. R. · 2 citations
Chemistry · Mathematics · Medicine · #57M25 #Bone health and treatments #FOS: Mathematics #Geometric and Algebraic Topology #Molecular spectroscopy and chirality #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:57M25
paper · pdf · doi:10.48550/arxiv.1012.3116
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
arxiv created 2010/12/14 · openalex publication_date 2010/12/14 · arxiv updated 2010/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.