A note on the special unitary group of a division algebra |
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| Authors: | B. A. Sethuraman B. Sury |
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| Affiliation: | Department of Mathematics, California State University Northridge, Northridge, California 91330 ; Stat-Math Unit, Indian Statistical Institute, 8th Mile Mysore Road, Bangalore 560 059, India |
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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  , ![$U(1,D)]$](http://www.ams.org/proc/2006-134-02/S0002-9939-05-07985-2/gif-abstract0/img4.gif) 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 ![$SU(1,D)/[U(1,d),U(1,D)]$](http://www.ams.org/proc/2006-134-02/S0002-9939-05-07985-2/gif-abstract0/img8.gif) can be infinite in general. We give an infinite class of examples. |
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