We define the notion of a principal S-bundle where S is a groupoid group bundle and show that there is a one-to-one correspondence between principal S-bundles and elements of a sheaf cohomology group associated to S. We also define the notion of a locally unitary action and show that the spectrum of the crossed product is a principal b S-bundle. Furthermore, we prove that the isomorphism class ...

Bounded orbit injection equivalence is an equivalence relation defined on minimal free Cantor systems which is a candidate to generalize flip Kakutani equivalence to actions of the Abelian free groups on more than one generator. This paper characterizes bounded orbit injection equivalence in terms of a mild strengthening of Rieffel-Morita equivalence of the associated C*-crossed-product algebra...

We introduce the labelling map and the quasi-free action of a locally compact abelian group on a graph C∗-algebra of a row-finite directed graph. Some necessary conditions for embedding the crossed product to an AF algebra are discussed, and one sufficient condition is proved that if the row-finite directed graph is constructed by possibly attaching some 1-loops to a row-finite directed graph w...

We compute the C*-algebra generated by a group of composition operators acting on certain reproducing kernel Hilbert spaces over the disk, where the symbols belong to a non-elementary Fuchsian group. We show that such a C*-algebra contains the compact operperators, and its quotient is isomorphic to the crossed product C*-algebra determined by the action of the group on the boundary circle. In a...

The relation between crossed product and H-Galois extension in braided tensor categories is established. It is shown that A = B#σH is a crossed product algebra if and only if the extension A/B is Galois, the inverse can of the canonical morphism can factors through object A⊗B A and A is isomorphic as left B-modules and right H-comodules to B⊗H in braided tensor categories. For the Yetter-Drinfe...

It is known that the Alamouti code is the only complex orthogonal design (COD) which achieves capacity and that too for the case of two transmit and one receive antenna only. Damen et al. proposed a design for 2 transmit antennas, which achieves capacity for any number of receive antennas, calling the resulting STBC when used with a signal set an informationlossless STBC. In this paper, using c...

Suppose that G is a groupoid acting on a small category H in the sense of [9, Definition 4] and H ×α G is the resulting semi-direct product category (as in [9, Proposition 8]). We show that there exists a subcategory Hr ⊆ H satisfying some nice property called “regularity” such that Hr ×α G = H ×α G. Moreover, we show that there exists a so-called “quasi action” (see Definition 3.1) β of G on C...

The problem of determining when a (classical) crossed product T = S ∗ G of a finite group G over a discrete valuation ring S is a maximal order, was answered in the 1960’s for the case where S is tamely ramified over the subring of invariants S. The answer was given in terms of the conductor subgroup (with respect to f) of the inertia. In this paper we solve this problem in general when S/S is ...

In this note, we will point out, as a corollary of Popa’s rigidity theory, that the crossed product von Neumann algebras for Bernoulli shifts cannot have relative property T. This is an operator algebra analogue of the theorem shown by Neuhauser and Cherix-Martin-Valette for discrete groups. Our proof is different from that for groups.

The notion of a multiplier of a group X is generalized to that of a C-multiplier by allowing it to have values in an arbitrary C-algebra A. On the other hand, the notion of the action of X in A is generalized to that of a projective action of X as linear transformations of the space of continuous functions with compact support in X and with values in A. It is shown that there exists a one-to-on...