广义Temperly-Lieb代数的胞腔基与Mahler测度
A cellular basis for the generalized Temperly-Lieb Algebra and Mahler Measure
摘要：
正如Temperley-Lieb代数是计算琼斯多项式的好地方，在边界上具有$2k$着色点的圆盘的Kauffman括号串代数，每个点都具有颜色$n$，是计算$n^{th}$着色琼斯多项式的好地方。在这里，这个彩色绞代数是一个细胞代数和一组分离的Jucys-Murphy元素。这是通过明确提供细胞基础和JM元素来完成的。这样做了几个结果的Mathas在这样的代数被认为是，包括建设成对的非同构不可约子模和它们相应的原始幂等元。这些幂等元，然后用来定义递归元素的彩色绞代数。递归元素是特别感兴趣的，因为它们已被用来将链接图的几何性质与琼斯多项式的马勒测度联系起来。特别地，给出了Champanerkar和Kofman的结果的一个证明，即Jones多项式和有色Jones多项式的Mahler测度在扭曲下收敛于一定数量的股。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
