C*-pseudo-multiplicative unitaries and Hopf C*-bimodules

We introduce C*-pseudo-multiplicative unitaries and concrete Hopf C*-bimodules for the study of quantum groupoids in the setting of C*-algebras. These unitaries and Hopf C*-bimodules generalize multiplicative unitaries and Hopf C*-algebras and are analogues of the pseudo-multiplicative unitaries and Hopf--von Neumann-bimod-ules studied by Enock, Lesieur and Vallin. To each C*-pseudo-multiplicative unitary, we associate two Fourier algebras with a duality pairing, a C*-tensor category of representations, and in the regular case two reduced and two universal Hopf C*-bimodules. The theory is illustrated by examples related to locally compact Hausdorff groupoids. In particular, we obtain a continuous Fourier algebra for a locally compact Hausdorff groupoid.Comment: 50 pages; this is a substantial revision and expansion of the preprint "C*-pseudo-multiplicative unitaries" (arXiv:0709.2995) with many new result

Coactions of Hopf C*-bimodules

Coactions of Hopf C*-bimodules simultaneously generalize coactions of Hopf C*-algebras and actions of groupoids. Following an approach of Baaj and Skandalis, we construct reduced crossed products and establish a duality for fine coactions. Examples of coactions arise from Fell bundles on groupoids and actions of a groupoid on bundles of C*-algebras. Continuous Fell bundles on an etale groupoid correspond to coactions of the reduced groupoid algebra, and actions of a groupoid on a continuous bundle of C*-algebras correspond to coactions of the function algebra.Comment: 44 pages, to appear in the Journal of Operator theor

The Breeder’s Eye – Theoretical Aspects of the Breeder’s Decision-Making

The report describes an empirical research project which investigated the peculiarity and role of knowledge gained through experience in plant breeding from the breeder’s perspective. In this paper, a theory respecting the breeder’s decision-making process will be presented. The categories of knowledge that are important for the decision-making process will be sketched and three levels of consciousness elaborated. The integration of all levels of knowledge and consciousness is what in the end determines whether the breeder’s decision-making activities are competent or not. This complexity is defined as intuition in the sense of an invariant present. The empirical findings will be briefly discussed with respect to their importance to organic agricultural science and organic plant breeding

The Fell compactification and non-Hausdorff groupoids

A compactification of Fell is applied to locally compact non-Hausdorff groupoids and yields locally compact Hausdorff groupoids. In the etale case, this construction provides a geometric picture for the left-regular representations introduced by Khoshkam and Skandalis.Comment: 7 page