Free limits of free algebras

被引：0

作者：

Chirvasitu, Alexandru ^{[1
]}

Hong, Tao ^{[2
]}

机构：

[1] Univ Buffalo, Dept Math, Buffalo, NY 14260 USA

[2] Xianyang Normal Univ, Sch Math & Stat, Xianyang 712000, Peoples R China

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2024年 / 228卷 / 05期

基金：

美国国家科学基金会;

关键词：

Lie polynomial; Free Lie algebra; Graded Lie algebra; Free algebra; Weak algorithm; Unrestricted coproduct; BIG POLYNOMIAL-RINGS;

D O I：

10.1016/j.jpaa.2023.107559

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consider a diagram center dot center dot center dot-+ F3-+ F2-+ F1 of algebraic systems, where Fn denotes the free object on n generators and the connecting maps send the extra generator to some distinguished trivial element. We prove that (a) if the Fi are free associative algebras over a fixed field then the limit in the category of graded algebras is again free on a set of homogeneous generators; (b) on the other hand, the limit in the category of associative (ungraded) algebras is a free formal power series algebra on a set of homogeneous elements, and (c) if the Fi are free Lie algebras then the limit in the category of graded Lie algebras is again free.(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：12