Geometric group theory | Representation theory

Haagerup property

In mathematics, the Haagerup property, named after Uffe Haagerup and also known as Gromov's a-T-menability, is a property of 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 embeddable into a Hilbert space. (Wikipedia).

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Related pages

Proper map | Continuous function | Group (mathematics) | Kazhdan's property (T) | Trivial representation | Cubical complex | Representation theory | Positive-definite function on a group | Mathematics | Function (mathematics) | Coxeter group | Embedding | Amenable group | Operator K-theory | Compact group | Geometric group theory | Hilbert space | Novikov conjecture | Unitary representation | Uniform convergence | Baum–Connes conjecture | Harmonic analysis | Locally compact group