CLASSIFICATION OF ACTIONS OF COMPACT GROUPS ON REAL APPROXIMATELY FINITE DIMENSIONAL C*-ALGEBRAS

摘要

A K-theoretic classification is given of actions of compact groups on real C*-algebras arising as inductive limits of actions on finite dimensional real C*-algebras. The invariant consists of the K-0 groups of the crossed products of the real algebra, its complexification, and its tensor product with the quaternions, by the action, and the maps between them induced by the natural inclusions of the real algebra into the complexification and the complexification to the tensor product with the quaternions. Here, the K-0 groups are viewed as ordered groups with distinguished elements, and the K0 of the complexification is given the structure of a module over the K0 of the group C*-algebra.