S. Kaliszewski

Hecke C*-algebras and semi-direct products

A Hecke pair (G,H) comprises a group G and a subgroup H for which every double coset is a finite union of left cosets, and the associated Hecke algebra, generated by the characteristic functions of double cosets, reduces to the group ∗-algebra of G/H when H is normal. In [4] we introduced the Schlichting completion as a tool for analyzing Hecke algebras, based in part upon work of Tzanev [13]. (A slight variation on this construction appears in [14].) The idea is that H is a compact open subgroup of G such that the Hecke algebra of (G,H) is naturally identified with the Hecke algebra H of (G,H). The characteristic function p of H is a projection in the group C∗-algebra A := C∗(G), and H can be identified with pCc(G)p ⊆ A; thus closure of H in A coincides with the corner pAp, which is Morita-Rieffel equivalent to the ideal ApA. In [4] we were mainly interested in studying when pAp is the enveloping C∗-algebra of the Hecke algebra H, and when the projection p is full in A, making the C∗-completion pAp ofHMorita-Rieffel equivalent to the group C∗-algebra A. We had most success when G = N o Q was a semidirect product with H contained in the normal subgroup N . In this paper we again consider G = N o Q, but now we allow the Hecke subgroup H to be spread across both N and Q. This leads to a refinement of the Morita-Rieffel equivalence ApA ∼ MR pAp (see

TOPOLOGICAL REALIZATIONS AND FUNDAMENTAL GROUPS OF HIGHER-RANK GRAPHS

We investigate topological realizations of higher-rank graphs. We show that the fundamental group of a higher-rank graph coincides with the fundamental group of its topological realization. We also show that topological realization of higher-rank graphs is a functor, and that for each higher-rank graph Lambda, this functor determines a category equivalence between the category of coverings of Lambda and the category of coverings of its topological realization. We discuss how topological realization relates to two standard constructions for k-graphs: projective limits and crossed products by finitely generated free abelian groups.

Rigidity theory for C∗-dynamical systems and the “Pedersen rigidity problem”

Let G be a locally compact abelian group. By modifying a theorem of Pedersen, it follows that actions of G on C∗-algebras A and B are outer conjugate if and only if there is an isomorphism of the c...

DUALITIES FOR MAXIMAL COACTIONS

We present a new construction of crossed-product duality for maximal coactions that uses Fischers work on maximalizations. Given a group

Erratum to “Full and reduced C*-coactions”. Math. Proc. Camb. Phil. Soc. 116 (1994), 435–450

G

Equivariance and imprimivity for discrete hopf c*-coactions

and a coaction

Coaction functors, II

(A,delta)

A new look at crossed product correspondences and associated C*-algebras

we define a generalized fixed-point algebra as a certain subalgebra of

Coactions on Cuntz-Pimsner Algebras

M(Artimes_{delta} G rtimes_{widehat{delta}} G)

Properness conditions for actions and coactions

, and recover the coaction via this double crossed product. Our goal is to formulate this duality in a category-theoretic context, and one advantage of our construction is that it breaks down into parts that are easy to handle in this regard. We first explain this for the category of nondegenerate *-homomorphisms, and then analogously for the category of