Projectors in the Virtual Temperley-Lieb Algebra
Qingying Deng, Xian'an Jin, Louis H. Kauffman
TL;DR
This paper introduces a generalized method for defining projectors in the virtual Temperley-Lieb algebra, extending Jones-Wenzl projectors with additional properties related to virtual generators.
Contribution
It presents a new construction of projectors in the virtual Temperley-Lieb algebra, including their explicit formulas and uniqueness properties.
Findings
Projectors have properties similar to Jones-Wenzl projectors.
An extra property involving virtual generators is identified.
Explicit formulas for the projectors are derived.
Abstract
We present a method of defining projectors in the virtual Temperley-Lieb algebra, that generalizes the Jones-Wenzl projectors in Temperley-Lieb algebra. We show that the projectors have similar properties with the Jones-Wenzl projectors, and contain an extra property which is associated with the virtual generator elements, that is, the product of a projector with a virtual generator is unchanged. We also show the uniqueness of the projector in terms of its axiomatic properties in the virtual Temperley-Lieba algebra . Finally, we find the coefficients of and give an explicit formula for the projector .
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models