A fundamental property of Suslin matrices

Jose, Selby ; Rao, Ravi A. (2010) A fundamental property of Suslin matrices Journal of K-Theory, 5 (03). pp. 407-436. ISSN 1865-2433

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Official URL: https://www.cambridge.org/core/journals/journal-of...

Related URL: http://dx.doi.org/10.1017/is010005001jkt101

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.

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ID Code:107124
Deposited On:26 Dec 2017 11:21
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