Exotic Coactions

Full Crossed Products by Coactions,

Let δ be a coaction of a locally compact group G on a C*-algebra A. We show that if I is a δ-invariant ideal in A, then 0! I¬δ I G!A¬δ G! (A}I )¬δI G! 0 for full crossed products, as Landstad et al. have done for spatial crossed products by coactions. We prove that for suitable coactions, the crossed products of C ! (X )-algebras are again C ! (X )-algebras, and the crossed products of continuo...

Weakly multiplicative coactions of quantized function algebras

A condition is identified which guarantees that the coinvariants of a coaction of a Hopf algebra on an algebra form a subalgebra, even though the coaction may fail to be an algebra homomorphism. A Hilbert Theorem (finite generation of the subalgebra of coinvariants) is obtained for such coactions of a cosemisimple Hopf algebra. This is applied for two coactions α, β : A → A⊗O, where A is the co...

Skew Products and Crossed Products by Coactions

Given a labeling c of the edges of a directed graph E by elements of a discrete group G, one can form a skew-product graph E ×c G. We show, using the universal properties of the various constructions involved, that there is a coaction δ of G on C∗(E) such that C∗(E ×c G) is isomorphic to the crossed product C ∗(E) ×δ G. This isomorphism is equivariant for the dual action δ̂ and a natural action ...

Exotic Atoms and Exotic Nuclei

Induced C* -algebras and Landstad Duality for Twisted Coactions

Suppose N is a closed normal subgroup of a locally compact group G. A coaction e: A —» M(A ® C*(N)) of N on a C*-algebra A can be inflated to a coaction S of G on A , and the crossed product A x¿ G is then isomorphic to the induced C*-algebra Ind^A xe N . We prove this and a natural generalization in which A xf N is replaced by a twisted crossed product A x G/N G ; in case G is abelian, we reco...