An algebra-level version of a link-polynomial identity of Lickorish

Details An algebra-level version of a link-polynomial identity of Lickorish An algebra-level version of a link-polynomial identity of Lickorish

2006-05-16

arxiv.org/abs/math/0605455v1

Math. Proc. Cambridge Philos. Soc. vol. 144, no. 3, (2008), 623--638.

Mathematics

Quantum Algebra

21 pages, 2 figures

Scientific paper

We establish isomorphisms between certain specializations of
Birman-Murakami-Wenzl algebras and the symmetric squares of Temperley-Lieb
algebras. These isomorphisms imply a link-polynomial identity due to W. B. R.
Lickorish. As an application, we compute the closed images of the irreducible
braid group representations factoring over these specialized BMW algebras.

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