Representation Theory for Subfactors, $${\lambda}$$λ-Lattices and C*-Tensor Categories

By Sorin Popa, S. Vaes. 2014

47 citations recorded by the source corpus.

We develop a representation theory for $${\lambda}$$λ-lattices, arising as standard invariants of subfactors, and for rigid C*-tensor categories, including a definition of their universal C*-algebra. We use this to give a systematic account of approximation and rigidity properties for subfactors and tensor categories, like (weak) amenability, the Haagerup property and property (T). We determine all unitary representations of the Temperley–Lieb–Jones $${\lambda}$$λ-lattices and prove that they have the Haagerup property and the complete metric approximation property. We also present the first subfactors with property (T) standard invariant and that are not constructed from property (T) groups.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/61de89fc557dfdf1d7d15ddef57a5c830fde5c55

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In Algebra and Number Theory

In Geometry and Topology

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Citations in the corpus

Drinfeld Center and Representation Theory for Monoidal Categories (2015, methodology): “ character algebra constructed from the spherical representations of the Drinfeld double, as observed in [DCFY14]. Such a categoriﬁcation has been already obtained in the recent work of Popa and Vaes [PV15], and similarly to their work our main motivation is to understand approximation properties of”
Cohomology and $L^2$-Betti numbers for subfactors and quasi-regular inclusions (2015, methodology): “enoting by C the tensor category of M-bimodules generated by N ⊂ M, the notions of an admissible state on the fusion ∗-algebra C[C] (see (2.6)) and an admissible representation of C[C] were deﬁned in [PV14] and characterized purely in terms of C as a rigid C∗-tensor category. It was proved that ther”