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A Fundamental Property of Suslin Matrices

Published online by Cambridge University Press:  03 June 2010

Selby Jose  and
Ravi A. Rao
Selby Jose
Affiliation:
Department of Mathematics, Ismail Yusuf College, Jogeshwari(E), Mumbai 400-060, selbyjose@rediffmail.com.
Ravi A. Rao
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Dr. Homi Bhabha Road, Mumbai 400 005, ravi@math.tifr.res.in.
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Abstract

We describe a homomorphism from the group SUmr (R), generated by Suslin matrices, when r is even, to the special orthogonal group SO2(r+1) (R) by relating the Suslin matrix corresponding to a pair of vectors v, w, with 〈v, w〉 = 1, to the product of two reflections, one w.r.t. the vectors v, w and the other w.r.t. the vectors e1, e1 (of length one). When r is odd we can still associate a product of reflections with an element of SUmr (R), which is well defined up to a unit u, with u2 = 1. This association enables one to study the orbit space of unimodular vectors under the elementary subgroup.

Keywords

Unimodular rowsorthogonal transformationsreflections

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Type
Research Article
Information
Journal of K-Theory , Volume 5 , Issue 3 , June 2010 , pp. 407 - 436
Copyright
Copyright © ISOPP 2010

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