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 is a division algebra with its center a number field and with an involution of the second kind, it is unknown if the group , is trivial. We show that, by contrast, if is a function field in one variable over a number field, and if is an algebra with center and with an involution of the second kind, the group 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

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