Weak amenability for subfactors

Arnaud Brothier

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arXiv · 1410.2875

Weak amenability for subfactors

Arnaud Brothier

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Abstract

We define the notions of weak amenability and the Cowling-Haagerup constant for extremal finite index subfactors of type II_1. We prove that the Cowling-Haagerup constant only depends on the standard invariant of the subfactor. Hence, we define the Cowling-Haagerup constant for standard invariants. We explicitly compute the constant for Bisch-Haagerup subfactors and prove that it is equal to the constant of the group involved in the construction. Given a finite family of amenable standard invariants in the sense of Popa, we prove that their free product in the sense of Bisch-Jones is weakly amenable with constant 1. We show that the Cowling-Haagerup constant of the tensor product of a finite family of standard invariants is equal to the product of their Cowling-Haagerup constants.

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BibTeX RIS

Arnaud Brothier. 2015-03-30. Weak amenability for subfactors. https://arxiv.org/abs/1410.2875

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