DSER初等正交群中换向子的瑜伽

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2018-11-15 DOI:10.1007/s40062-018-0223-5

A. A. Ambily

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引用次数: 2

摘要

本文研究了Roy在交换环上引入的具有双曲和的非退化二次空间的正交群的Dickson-Siegel-Eichler-Roy (DSER)初等正交子群。证明了DSER初等正交群的初等生成元之间的一组交换子关系。作为一个应用，我们证明了这个群是完美的，并证明了这个群的Quillen局部-全局原理的一个动作版本。这肯定地回答了Rao博士论文中的一个问题。

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Yoga of commutators in DSER elementary orthogonal group

In this article, we consider the Dickson-Siegel-Eichler-Roy (DSER) elementary orthogonal subgroup of the orthogonal group of a non-degenerate quadratic space with a hyperbolic summand over a commutative ring, introduced by Roy. We prove a set of commutator relations among the elementary generators of the DSER elementary orthogonal group. As an application, we prove that this group is perfect and an action version of the Quillen’s local-global principle for this group is proved. This affirmatively answers a question of Rao in his Ph.D. thesis.

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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.