Index for C*-subalgebras

In this paper we study the index, denoted by Index [italic]E, for conditional expectations [italic]E on [italic]C*-algebras, which is a generalization of the index for subfactors by Jones and Kosaki. The notion of the index is related with coring structure, separable extension, generalized Casimir elements, G-Galois basis, covering spaces, modular automorphisms and Nakayama automorphisms on Frobenius algebras.