Weak amenability for subfactors

作者：Brothier Arnaud^*

来源：International Journal of Mathematics, 2015, 26(7): 1550048.

DOI：10.1142/S0129167X15500482

• Weak amenability
• subfactors
• Cowling-Haagerup constants
• standard invariants
• type II1 factors

We define the notions of weak amenability and the Cowling-Haagerup constant for extremal finite index subfactors of type II1. 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, 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.

• 出版日期2015-6