The invariant continuous-trace C*-algebras by the actions of compact Abelian groups

The author studies the relation of continuous-trace property between C*-algebra A and the fixed point C*-algebra A(alpha) in certain C*-dynamic system (A, G, alpha) by introducing an a-invariant continuous trace property. For separable C*-dynamic system (A, G, alpha) with G compact and abelian, A liminal, alpha(t) is an element of Aut(Cb)((A) over cap) and pointwise unitary, the necessary and sufficient condition for A to be continuous-trace, which contains A(alpha) continuous-trace, is obtained.