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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A stably elementary homotopy


Author: Ravi A. Rao
Journal: Proc. Amer. Math. Soc. 137 (2009), 3637-3645
MSC (2000): Primary 13C10, 19D45, 19G12, 55Q55
Published electronically: June 16, 2009
MathSciNet review: 2529870
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Abstract: If $ R$ is an affine algebra of dimension $ d$ over a perfect C$ _1$ field and $ \sigma \in SL_{d + 1}(R)$ is a stably elementary matrix, we show that there is a stably elementary matrix $ \sigma(X) \in SL_{d + 1}(R[X])$ with $ \sigma(1) = \sigma$ and $ \sigma(0) = I_{d + 1}$.


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Additional Information

Ravi A. Rao
Affiliation: Tata Institute of Fundamental Research, Dr. Homi Bhabha Road, Navy Nagar, Mumbai 400 005, India
Email: ravi@math.tifr.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09949-3
PII: S 0002-9939(09)09949-3
Keywords: Unimodular row, stably elementary matrices, homotopy
Received by editor(s): November 12, 2007
Received by editor(s) in revised form: December 5, 2007, and February 27, 2009
Published electronically: June 16, 2009
Communicated by: Martin Lorenz
Article copyright: © Copyright 2009 American Mathematical Society