A Matsumoto type theorem for $GL_n$ over rings of non-commutative Laurent polynomials

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2024-04-06 DOI:10.1007/s40062-024-00345-6

Ryusuke Sugawara

引用次数: 0

Abstract

We give a Matsumoto-type presentation of $K_2$-groups over rings of non-commutative Laurent polynomials, which is a non-commutative version of M. Tomie’s result for loop groups. Our main idea is induced by U. Rehmann’s approach in the case of division rings.

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非交换月桂多项式环上 $$GL_n$$ 的松本类型定理

摘要我们给出了非交换劳伦特多项式环上的$K_2$ -群的松本类型表示，这是富江（M. Tomie）关于环群的结果的非交换版本。我们的主要想法是由 U. Rehmann 在划分环情况下的方法诱发的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.

A Matsumoto type theorem for \(GL_n\) over rings of non-commutative Laurent polynomials

Abstract