Chebyshev polynomials and the Frohman-Gelca formula

Hoel Queffelec; Heather M. Russell

doi:10.1142/S0218216515500236

Chebyshev polynomials and the Frohman-Gelca formula

Hoel Queffelec
, Heather M. Russell

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Using Chebyshev polynomials, C. Frohman and R. Gelca introduced a basis of the Kauffman bracket skein module of the torus. This basis is especially useful because the Jones-Kauffman product can be described via a very simple Product-to-Sum formula. Presented in this work is a diagrammatic proof of this formula, which emphasizes and demystifies the role played by Chebyshev polynomials.

Original language	English
Article number	1550023
Journal	Journal of Knot Theory and its Ramifications
Volume	24
Issue number	4
DOIs	https://doi.org/10.1142/S0218216515500236
Publication status	Published - 22 Apr 2015

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abstract = "Using Chebyshev polynomials, C. Frohman and R. Gelca introduced a basis of the Kauffman bracket skein module of the torus. This basis is especially useful because the Jones-Kauffman product can be described via a very simple Product-to-Sum formula. Presented in this work is a diagrammatic proof of this formula, which emphasizes and demystifies the role played by Chebyshev polynomials.",

keywords = "Chebyshev polynomials, Frohman-Gelca formula, Jones-Kauffman algebra, Skein module, Torus",

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AB - Using Chebyshev polynomials, C. Frohman and R. Gelca introduced a basis of the Kauffman bracket skein module of the torus. This basis is especially useful because the Jones-Kauffman product can be described via a very simple Product-to-Sum formula. Presented in this work is a diagrammatic proof of this formula, which emphasizes and demystifies the role played by Chebyshev polynomials.

KW - Chebyshev polynomials

KW - Frohman-Gelca formula

KW - Jones-Kauffman algebra

KW - Skein module

KW - Torus

UR - https://www.scopus.com/pages/publications/84929607250

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DO - 10.1142/S0218216515500236

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ER -

Chebyshev polynomials and the Frohman-Gelca formula

Abstract

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