SIMPLE ALGEBRAS WITH INVOLUTION, AND UNITARY GROUPS

Let A be a central simple algebra on which an involutory antiautomorphism S is given whose restriction to the center K of A is not the identity. Let ?(A*) be the subgroup of the multiplicative group A* of A generated by the elements x A* such that xS = x, let NrdA/K : ?A?K be the reduced norm mapping of A into K, and let ? '(A*) be the subgroup of A* generated by the elements x A* whose reduced norm is invariant with respect to S. This paper considers the problem of when the groups ? '(A*) and ?(A*) coincide. Bibliography: 15 titles.