A note on the special unitary group of a division algebra

Sethuraman, B.; Sury, B.

doi:10.1090/S0002-9939-05-07985-2

A note on the special unitary group of a division algebra
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by B. A. Sethuraman and B. Sury PDF

Proc. Amer. Math. Soc. 134 (2006), 351-354 Request permission

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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