A structure theorem for the elementary unimodular vector group

Authors:
Selby Jose and Ravi A. Rao

Journal:
Trans. Amer. Math. Soc. **358** (2006), 3097-3112

MSC (2000):
Primary 13D15, 15A66, 19A15, 19E20, 55Q55

Published electronically:
October 31, 2005

MathSciNet review:
2216260

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a pair of vectors with , A. Suslin constructed a matrix . We study the subgroup generated by these matrices, and its (elementary) subgroup generated by the matrices , for . The basic calculus for is developed via a key lemma, and a fundamental property of Suslin matrices is derived.

**1.**Jose, S., Rao R. A.,*A local global principle for the elementary unimodular vector group*, Commutative Algebra and Algebraic Geometry (Bangalore, India, 2003), Contemp. Math., vol. 390, Amer. Math. Soc., Providence, RI, 2005, pp. 119-125.**2.**Rao, R. A., Jose, S.,*A fundamental property of Suslin matrices*, in preparation.**3.**L. N. Vaseršteĭn and A. A. Suslin,*Serre’s problem on projective modules over polynomial rings, and algebraic 𝐾-theory*, Izv. Akad. Nauk SSSR Ser. Mat.**40**(1976), no. 5, 993–1054, 1199 (Russian). MR**0447245****4.**A. A. Suslin,*Stably free modules*, Mat. Sb. (N.S.)**102(144)**(1977), no. 4, 537–550, 632 (Russian). MR**0441949****5.**A. A. Suslin,*The structure of the special linear group over rings of polynomials*, Izv. Akad. Nauk SSSR Ser. Mat.**41**(1977), no. 2, 235–252, 477 (Russian). MR**0472792**

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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

DOI:
https://doi.org/10.1090/S0002-9947-05-03794-3

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

Article copyright:
© Copyright 2005
American Mathematical Society