发表机构
Central University of Rajasthan; University of Allahabad; Ewing Christian College（中央拉贾斯坦大学; 阿拉哈巴德大学; 尤因基督学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为泛交换子恒等式赋予正式含义，引入高阶Schur乘子，研究Steinberg与Chevalley乘法李代数及其自由结构，探讨其在描述泛交换子恒等式中的作用。
AI 中文摘要
本文旨在为泛交换子恒等式赋予正式含义，并探究群上的乘法李代数结构为何是描述泛交换子恒等式的潜在候选对象。我们引入若干高阶Schur乘子，同时介绍并研究Steinberg与Chevalley乘法李代数，这类乘法李代数的根向量间具有描述李乘积关系的交换子恒等式，还讨论了Steinberg群与Chevalley群上的自由乘法李代数。
英文摘要
The aim of this paper is to give a formal meaning of universal commutator identities and to see as to how the structure of multiplicative Lie algebra on a group is a potential candidate to describe universal commutator identities. We introduce some higher Schur multipliers. We shall also introduce and study Steinberg and Chevalley Multiplicative Lie algebras, the multiplicative Lie algebras with commutator identities among the root vectors describing Lie product relations. Free multiplicative Lie algebra on Steinberg and Chevalley groups are discussed.
