Virtual Extension of Temperley--Lieb Algebra

Details Virtual Extension of Temperley--Lieb Algebra Virtual Extension of Temperley--Lieb Algebra

2006-10-22

arxiv.org/abs/math-ph/0610052v1

Physics

Mathematical Physics

10 pages, latex

Scientific paper

The virtual knot theory is a new interesting subject in the recent study of low dimensional topology. In this paper, we explore the algebraic structure underlying the virtual braid group and call it the virtual Temperley--Lieb algebra which is an extension of the Temperley--Lieb algebra by adding the group algebra of the symmetrical group. We make a connection clear between the Brauer algebra and virtual Temperley--Lieb algebra, and show the algebra generated by permutation and its partial transpose to be an example for the virtual Temperley--Lieb algebra and its important quotients.

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