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Just as the Temperley-Lieb algebra is a good place to compute the Jonespolynomial, the Kauffman bracket skein algebra of a disk with $2k$ coloredpoints on the boundary, each with color $n$, is a good place to compute the$n^{th}$ colored Jones polynomial. Here, this colored skein algebra is shown tobe a cellular algebra and a set of separating Jucys-Murphy elements isprovided. This is done by explicitly providing the cellular basis and theJM-elements. Having done this several results of Mathas on such algebras areconsidered, including the construction of pairwise non-isomorphic irreduciblesubmodules and their corresponding primitive idempotents. These idempotents arethen used to define recursive elements of the colored skein algebra. Recursiveelements are of particular interest as they have been used to relate geometricproperties of link diagrams to the Mahler measure of the Jones polynomial. Inparticular, a single proof is given for the result of Champanerkar and Kofman,that the Mahler measure of the Jones and colored Jones polynomial convergesunder twisting on some number of strands.

A cellular basis for the generalized Temperly-Lieb Algebra and Mahler Measure