论文标题
lyndon单词的量子组代数的基础
Bases of Quantum Group Algebras in Terms of Lyndon Words
论文作者
论文摘要
我们已经回顾了一些量化的改组，尤其是该代数的分级和结构。同时，我们总结了有关古典洗牌代数的某些细节，包括林登单词（素数）和以林登·词的形式构建古典洗牌代数的基础。我们已经解释了如何根据lyndon单词来使该理论适应量子群代数的基础。该方法对量子组参数的特定情况有限，是统一的根源，要求对统一根的专业化是不受限制的。作为这项工作的另一个应用的部分，我们实施了一个Wolfram Mathematica软件包，该软件包具有用于量子shuffle乘法和基础构造的函数。
We have reviewed some results on quantized shuffling, and in particular, the grading and structure of this algebra. In parallel, we have summarized certain details about classical shuffle algebras, including Lyndon words (primes) and the construction of bases of classical shuffle algebras in terms of Lyndon words. We have explained how to adapt this theory to the construction of bases of quantum group algebras in terms of Lyndon words. This method has a limited application to the specific case of the quantum group parameter being a root of unity, with the requirement that specialization to the root of unity is non-restricted. As an additional, applied part of this work, we have implemented a Wolfram Mathematica package with functions for quantum shuffle multiplication and constructions of bases in terms of Lyndon words.
