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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 note on the special unitary group of a division algebra


Authors: B. A. Sethuraman and B. Sury
Journal: Proc. Amer. Math. Soc. 134 (2006), 351-354
MSC (2000): Primary 16K20, 12E15
Published electronically: July 7, 2005
MathSciNet review: 2176001
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Abstract: If $D$ is a division algebra with its center a number field $K$ and with an involution of the second kind, it is unknown if the group $SU(1,D)/[U(1,d)$, $U(1,D)]$ is trivial. We show that, by contrast, if $K$is a function field in one variable over a number field, and if $D$ is an algebra with center $K$ and with an involution of the second kind, the group $SU(1,D)/[U(1,d),U(1,D)]$ can be infinite in general. We give an infinite class of examples.


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Additional Information

B. A. Sethuraman
Affiliation: Department of Mathematics, California State University Northridge, Northridge, California 91330
Email: al.sethuraman@csun.edu

B. Sury
Affiliation: Stat-Math Unit, Indian Statistical Institute, 8th Mile Mysore Road, Bangalore 560 059, India
Email: sury@isibang.ac.in

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07985-2
PII: S 0002-9939(05)07985-2
Received by editor(s): April 19, 2004
Received by editor(s) in revised form: September 21, 2004
Published electronically: July 7, 2005
Additional Notes: This work was done when the first-named author visited the Indian Statistical Institute, Bangalore. He thanks the Institute for the wonderful hospitality it showed during his stay there.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2005 American Mathematical Society