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A basis for the Birman-Wenzl algebra

Morton, H.R. (2010) A basis for the Birman-Wenzl algebra. (Unpublished)

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This paper provides an explicit isomorphism between the Birman- Wenzl algebra BWn, constructed by J. Birman and H. Wenzl, and the Kauffman algebra MTn, subsequently constructed by H.R. Morton and P. Traczyk. The Birman-Wenzl algebra is defined algebraically using generators and relations while the Kauffman algebra has a geometric formulation in terms of tangles. The isomorphism is obtained by constructing an explicit basis in BWn, analogous to a basis previously constructed for MTn using ‘Brauer connectors’. The geometric isotopy arguments used for MTn are systematically replaced by algebraic versions using the Birman-Wenzl relations. This not only gives a direct way of determining the dimension of the Birman-Wenzl algebra, but also clarifies the role played by the ring of coefficients, �, and its specialisations.

Item Type:Article
Additional Information:ARXIV NUMBER: arXiv:1012.3116v1 [math.QA]. Date: December 14, 2010 (date deposited in ArXiv). Draft version only as paper unpublished.
Subjects:Q Science > QA Mathematics
Departments, Research Centres and Related Units:Academic Faculties, Institutes and Research Centres > Faculty of Science > Department of Mathematical Sciences
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ID Code:1477
Deposited On:23 Dec 2011 15:45
Last Modified:04 May 2012 17:45

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