Jones多项式的一个推广
An adelic extension of the Jones polynomial
摘要：
本文给出了Yokonuma-Hecke代数和Adelic Yokonuma-Hecke代数中的经典辫。更确切地说，我们定义的框架辫群的完成，我们介绍了adelic Yokonuma-Hecke代数，在类比的$p$-进框架辫子和$p$ -进Yokonuma-Hecke代数在\cite{jula,jula2}介绍。我们进一步构造了一个类似于\cite{jula2}中构造的$p$-adic马尔可夫迹的adelic马尔可夫迹，并利用\cite{ju}中的迹和adelic马尔可夫迹，在一定条件下定义了经典节点和链路的拓扑不变量.每个不变量满足来自Yokonuma-Hecke代数的三次绞关系。
英文摘要：
In this paper we represent the classical braids in the Yokonuma--Hecke and the adelic Yokonuma--Hecke algebras. More precisely, we define the completion of the framed braid group and we introduce the adelic Yokonuma--Hecke algebras, in analogy to the $p$--adic framed braids and the $p$--adic Yokonuma--Hecke algebras introduced in \cite{jula,jula2}. We further construct an adelic Markov trace, analogous to the $p$--adic Markov trace constructed in \cite{jula2}, and using the traces in \cite{ju} and the adelic Markov trace we define topological invariants of classical knots and links, upon imposing some condition. Each invariant satisfies a cubic skein relation coming from the Yokonuma--Hecke algebra.
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