  Just as the Temperley-Lieb algebra is a good place to compute the Jones
polynomial, the Kauffman bracket skein algebra of a disk with $2k$ colored
points 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 to
be a cellular algebra and a set of separating Jucys-Murphy elements is
provided. This is done by explicitly providing the cellular basis and the
JM-elements. Having done this several results of Mathas on such algebras are
considered, including the construction of pairwise non-isomorphic irreducible
submodules and their corresponding primitive idempotents. These idempotents are
then used to define recursive elements of the colored skein algebra. Recursive
elements are of particular interest as they have been used to relate geometric
properties of link diagrams to the Mahler measure of the Jones polynomial. In
particular, a single proof is given for the result of Champanerkar and Kofman,
that the Mahler measure of the Jones and colored Jones polynomial converges
under twisting on some number of strands.
