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Published in:
A Survey of Hyperbolic Knot Theory Read chapter Read first chapter

2019 | OriginalPaper | Chapter

From the Framisation of the Temperley–Lieb Algebra to the Jones Polynomial: An Algebraic Approach

Author : Maria Chlouveraki

Published in: Knots, Low-Dimensional Topology and Applications

Publisher: Springer International Publishing

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Abstract

We prove that the Framisation of the Temperley–Lieb algebra is isomorphic to a direct sum of matrix algebras over tensor products of classical Temperley–Lieb algebras. We use this result to obtain a closed combinatorial formula for the invariants for classical links obtained from a Markov trace on the Framisation of the Temperley–Lieb algebra. For a given link L, this formula involves the Jones polynomials of all sublinks of L, as well as linking numbers.

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previous chapter Extending the Classical Skein
next chapter A Note on Link Invariants and the HOMFLY–PT Polynomial
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Metadata
Title
From the Framisation of the Temperley–Lieb Algebra to the Jones Polynomial: An Algebraic Approach
Author
Maria Chlouveraki
Copyright Year
2019
Book
Knots, Low-Dimensional Topology and Applications

Print ISBN: 978-3-030-16030-2

Electronic ISBN: 978-3-030-16031-9

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-16031-9_12

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