SIMPLICITY OF THE PROJECTIVE UNITARY GROUP OF THE MULTIPLIER ALGEBRA OF A SIMPLE STABLE NUCLEAR C*-ALGEBRA

If A is a unital simple separable nuclear C*-algebra with real rank zero, then U(M(A circle times K))/T, given the quotient topology induced by the strict topology on U(M(A circle times K)) , is a simple topological group. Here, U(M(A circle times K)) is the unitary group of the multiplier algebra of the stabilization of A. T is the subgroup of scalar unitaries.) If A is a unital simple separable C*-algebra, then U(A)/T, given the quotient topology induced by the relative weak topology in U(A), is a simple topological group.