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Title: | Elementary Action of Classical Groups on Unimodular Rows Over Monoid Rings |
Authors: | BASU, RABEYA MATHEW, MARIA A. Dept. of Mathematics |
Keywords: | Monoid ring Classical group Unimodular row Elementary action Milnor patching Cancellative monoid K-1-stability 2024 2024-OCT-WEEK2 TOC-OCT-2024 |
Issue Date: | Oct-2024 |
Publisher: | Springer Nature |
Citation: | Transformation Groups |
Abstract: | The elementary action of symplectic and orthogonal groups on unimodular rows of length 2n is transitive for 2n >= max(4,d+2) in the symplectic case, and 2n >= max(6,2d+4) in the orthogonal case, over monoid rings R[M], where R is a commutative noetherian ring of dimension d, and M is commutative cancellative torsion free monoid. As a consequence, one gets the surjective stabilization bound for the K-1 for classical groups. This is an extension of J. Gubeladze's results for linear groups |
URI: | https://doi.org/10.1007/s00031-024-09883-y http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/9145 |
ISSN: | 1083-4362 1531-586X |
Appears in Collections: | JOURNAL ARTICLES |
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