Quillen--Suslin Theory; Revisited over Graded Rings release_ox3tq7gfwjgbnau4zh2docrfjy

by Rabeya Basu, Manish Kumar Singh

Released as a article .



In this paper we deduce a graded version of Quillen--Suslin's Local-Global Principle for the traditional classical groups, viz. general linear, symplectic and orthogonal groups and establish its equivalence of the normality property of the respective elementary subgroups. This generalizes previous result of Basu--Rao--Khanna. Then, as an application, we establish an analogue Local-Global Principle for the commutator subgroups of the special linear and symplectic groups. Finally, by using Swan-Weibel's homotopy trick, we establish graded analogue of the Local-Global Principle for the transvection subgroups of the full automorphism groups of the linear, symplectic and orthogonal modules. This generalizes the previous result of Bak--Basu--Rao.
In text/plain format

Archived Files and Locations

application/pdf  185.3 kB
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2018-11-02
Version   v1
Language   en ?
arXiv  1811.00725v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 761f4a5b-fb9d-48aa-8a4c-e8c0d495250a