论文标题
谎言代数，重写系统和Gröbner-Shirshov基地的操作员身份
Operator identities on Lie algebras, rewriting systems and Gröbner-Shirshov bases
论文作者
论文摘要
由线性操作员扮演的关键作用的激励，许多年前，Rota提议确定线性操作员在关联代数上满足的代数运算符身份，后来被称为Rota在代数运算符上的程序。该计划的最新进展是在操作的代数，重写系统和Groebner-Shirshov基地的背景下实现的。这些发展还表明，Rota的见解可以应用于代数上的操作员身份，从而使各种线性操作员以统一的角度将谎言代数置于Lie代数上。 本文采用了这种方法，利用了由非缔合的lyndon-shirshov单词跨越的操作多项式谎言代数。 ROTA程序的Lie代数类似物是根据融合重写系统制定的，并以Groebner-Shirshov基础等效。该谎言代数类似物与Rota的联想代数相兼容。作为应用程序，介绍了差分类型运算符和Rota-baxter操作员的分类。
Motivated by the pivotal role played by linear operators, many years ago Rota proposed to determine algebraic operator identities satisfied by linear operators on associative algebras, later called Rota's program on algebraic operators. Recent progresses on this program have been achieved in the contexts of operated algebra, rewriting systems and Groebner-Shirshov bases. These developments also suggest that Rota's insight can be applied to determine operator identities on Lie algebras, and thus to put the various linear operators on Lie algebras in a uniform perspective. This paper carries out this approach, utilizing operated polynomial Lie algebras spanned by non-associative Lyndon-Shirshov bracketed words. The Lie algebra analog of Rota's program was formulated in terms convergent rewriting systems and equivalently in terms of Groebner-Shirshov bases. This Lie algebra analog is shown to be compatible with Rota's program for associative algebras. As applications, a classification of differential type operators and Rota-Baxter operators are presented.
