179,166 research outputs found
K-theory for group C*-algebras
No full textThese notes are based on a lecture course given by the first author in the Sedano Winter School on K-theory held in Sedano, Spain, on January 22-27th of 2007. They aim at introducing K-theory of C*-algebras, equivariant K-homology and KK-theory in the context of the Baum-Connes conjectur
Spaces of graphs, boundary groupoids and the coarse Baum-Connes conjecture
No full textWe introduce a new variant of the coarse Baum–Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum–Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse Baum–Connes conjecture. In particular, we give a geometric proof of this conjecture for spaces of graphs that have large girth and bounded vertex degree. We then connect the boundary conjecture to the coarse Baum–Connes conjecture using homological methods, which allows us to exhibit all the current uniformly discrete counterexamples to the coarse Baum–Connes conjecture in an elementary way
The Baum-Connes conjecture for free orthogonal quantum groups
No full textWe prove an analogue of the Baum–Connes conjecture for free orthogonal quantum groups. More precisely, we show that these quantum groups have a γ-element and that γ=1. It follows that free orthogonal quantum groups are K-amenable. We compute explicitly their K-theory and deduce in the unimodular case that the corresponding reduced C<sup>⁎</sup>-algebras do not contain nontrivial idempotents.
Our approach is based on the reformulation of the Baum–Connes conjecture by Meyer and Nest using the language of triangulated categories. An important ingredient is the theory of monoidal equivalence of compact quantum groups developed by Bichon, De Rijdt and Vaes. This allows us to study the problem in terms of the quantum group SUq(2). The crucial part of the argument is a detailed analysis of the equivariant Kasparov theory of the standard Podleś sphere
Baum, Elmer C., D.O.
No full textAn Austin, Texas general practitioner since the mid-forties, Dr. Baum was responsible in part for TCOM’s success in receiving financial aid from the State of Texas. His political influence, as private physician to Governor Preston Smith, proved especially beneficial during the early years, 1966 to 1975.
Interviewed by C. Ray Stokes, October 5, 1989
Quantum SU(2) and the Baum-Connes conjecture
No full textWe review the formulation and proof of the Baum-Connes conjecture for the dual of the quantum group of Woronowicz. As an illustration of this result we determine the -groups of quantum automorphism groups of simple matrix algebras
The spin dependence of the excitation of metastable autoionising lithium 4P states by electron impact
No full textBaum G, Raith W, Schröder W. The spin dependence of the excitation of metastable autoionising lithium 4P states by electron impact. J.Phys. B. 1988;21(16):L501-L507
Measurement of spin asymmetries in the electron impact ionisation of alkali atoms
No full textBaum G, Moede M, Raith W, Schröder W. Measurement of spin asymmetries in the electron impact ionisation of alkali atoms. J.Phys. B. 1985;18(3):531-538
Inverse semigroups in coarse geometry
No full textInverse semigroups provide a natural way to encode combinatorial data from geometric settings. Examples of this occur in both geometry and topology, where the data comes in the form of partial bijections that preserve the topology, and operator algebras, where the partial bijections encode *-subsemigroups of partial isometries of Hilbert space. In this thesis we explore the connections between these two pictures within the backdrop of coarse geometry.The first collection of results is concerned primarily with inverse semigroups and their C*-algebras. We give a construction of a six term sequence of C*-algebras connecting the semigroup C*-algebra to that of a naturally associated group C*-algebra. This result is a generalisation of the ideas of Pimsner and Voiculescu, who were concerned with computing K-theory groups associated to actions of groups. We outline how to connect this picture, via groupoids, to that of a partial translation algebra of Brodzki, Niblo andWright, and further consider applications of these sequences to computations of certain K-groups associated with group and semigroup C*-algebras.Secondly, we give an account of the coarse Baum-Connes conjecture associated to a uniformly discrete bounded geometry metric space and rephrase the conjecture in terms of groupoids and their C*-algebras that can naturally be associated to a metric space. We then consider the well known counterexamples to this conjecture, giving a unifying framework for their study in terms of groupoids and a new conjecture for metric spaces that we call the boundary coarse Baum-Connes conjecture. Generalising a result of Willett and Yu we prove this conjecture for certain classes of expanders including those of large girth by constructing a partial action of a discrete group on such spaces
Geometric structure in smooth dual and local Langlands conjecture
No full textThis expository paper first reviews some basic facts about p-adic fields, reductive p-adic groups, and the local Langlands conjecture. If G is a reductive p-adic group, then the smooth dual of G is the set of equivalence classes of smooth irreducible representations of G. The representations are on vector spaces over the complex numbers. In a canonical way, the smooth dual is the disjoint union of subsets known as the Bernstein components. According to a conjecture due to ABPS (Aubert–Baum–Plymen–Solleveld), each Bernstein component has a geometric structure given by an appropriate extended quotient. The paper states this ABPS conjecture and then indicates evidence for the conjecture, and its connection to the local Langlands conjecture
Bredon homology and equivariant K-homology of SL(3,Z)
No full textWe obtain the equivariant K-homology of the classifying space underline{E}SL(3,Z) from the computation of its Bredon homology with respect to finite subgroups and coefficients in the representation ring. We also obtain the corresponding results for GL(3,Z). Our calculations give therefore the topological side of the Baum-Connes conjecture for these group
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