李代数的构型基及其对偶
The configuration basis of a Lie algebra and its dual
摘要：
我们使用李余代数和配置配对框架之前提出的Sinha和Walter推导出一个新的，左赋范单项式自由李代数的基础（从联想Lyndon-Shirshov字），以及一个对偶单项式李余代数的基础。我们的重点是通过使用配置框架和基础获得的计算灵活性。我们包括几个明确的例子，使用对偶余代数基础和配置配对进行李代数计算。作为推论，我们得到了shuffle代数的一个新的乘法基。
英文摘要：
We use the Lie coalgebra and configuration pairing framework presented previously by Sinha and Walter to derive a new, left-normed monomial basis for free Lie algebras (built from associative Lyndon-Shirshov words), as well as a dual monomial basis for Lie coalgebras. Our focus is on computational dexterity gained by using the configuration framework and basis. We include several explicit examples using the dual coalgebra basis and configuration pairing to perform Lie algebra computations. As a corollary of our work, we get a new multiplicative basis for the shuffle algebra.
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