On SU(1,D)/[U(1,D),U(1,D)] for a quaternion division algebra D
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Let D be a quaternion division algebra with an involution of the second kind. We show that the quotient group SU(1,D)/[U(1,D),U(1,D)] is nontrivial in general. For global fields, we completely determine this group.
Mathematics Subject Classification (2000).Primary 11R52
Keywords.Quaternion division algebra involution of the second kind unitary group
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