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Haagerup Property
In mathematics, the Haagerup property, named after Uffe Haagerup and also known as Mikhail Gromov (mathematician), Gromov's a-T-menability, is a property of Group (mathematics), groups that is a strong negation of Kazhdan's property (T). Property (T) is considered a representation-theoretic form of rigidity, so the Haagerup property may be considered a form of strong nonrigidity; see below for details. The Haagerup property is interesting to many fields of mathematics, including harmonic analysis, representation theory, operator K-theory, and geometric group theory. Perhaps its most impressive consequence is that groups with the Haagerup Property satisfy the Baum–Connes conjecture and the related Novikov conjecture. Groups with the Haagerup property are also uniformly embedding, embeddable into a Hilbert space. Definitions Let G be a second countable locally compact group. The following properties are all equivalent, and any of them may be taken to be definitions of the Haa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
