A structure theorem for the elementary unimodular vector group
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- by Selby Jose and Ravi A. Rao PDF
- Trans. Amer. Math. Soc. 358 (2006), 3097-3112 Request permission
Abstract:
Given a pair of vectors $v,w\in R^{r+1}$ with $\langle v,w\rangle =v\cdot w^T=1$, A. Suslin constructed a matrix $S_r(v,w)\in Sl_{2^r}(R)$. We study the subgroup $SUm_r(R)$ generated by these matrices, and its (elementary) subgroup $EUm_r(R)$ generated by the matrices $S_r(e_1\varepsilon ,e_1\varepsilon ^{T^{-1}})$, for $\varepsilon \in E_{r+1}(R)$. The basic calculus for $EUm_r(R)$ is developed via a key lemma, and a fundamental property of Suslin matrices is derived.References
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- Rao, R. A., Jose, S., A fundamental property of Suslin matrices, in preparation.
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Additional Information
- Selby Jose
- Affiliation: Department of Mathematics, Ismail Yusuf College, Jogeshwari(E), Mumbai 400-060, India
- Email: selbyjose@rediffmail.com
- Ravi A. Rao
- Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Dr. Homi Bhabha Road, Mumbai 400 005, India
- Email: ravi@math.tifr.res.in
- Received by editor(s): January 10, 2004
- Received by editor(s) in revised form: July 19, 2004
- Published electronically: October 31, 2005
- Additional Notes: This article is part of the first author’s doctoral dissertation
- © Copyright 2005 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 358 (2006), 3097-3112
- MSC (2000): Primary 13D15, 15A66, 19A15, 19E20, 55Q55
- DOI: https://doi.org/10.1090/S0002-9947-05-03794-3
- MathSciNet review: 2216260