Properly Outer and Strictly Outer Actions of Finite Groups on Prime C*-algebras

Abstract

An action of a compact, in particular finite group on a C*-algebra is called properly outer if no automorphism of the group that is distinct from identity is implemented by a unitary element of the algebra of local multipliers of the C*-algebra. In this paper I define the notion of strictly outer action (similar to the definition for von Neumann factors in [11]) and prove that for finite groups it is equivalent with proper outerness of the action. For finite abelian groups this is equivalent with other relevant properities of the action.

arXiv comment11 pages

References in corpus (1)

• Duality for compact group actions on operator algebras and applications: irreducible inclusions and Galois correspondence