Property (T) group factors whose Jones index set equals all positive integers
Ionut Chifan, Junhwi Lim

TL;DR
This paper constructs a continuum of property (T) factors with all positive integers as their Jones index set, using advanced techniques in deformation, rigidity, subfactor theory, and geometric group theory.
Contribution
It introduces new property (T) factors with all positive integer Jones indices, realized via group von Neumann algebras of generalized wreath-like product groups.
Findings
Existence of uncountably many non-stably isomorphic property (T) factors
Construction of factors with all positive integer Jones indices
Advancement of open question by P. de la Harpe
Abstract
Using a m\'elange of techniques at the rich intersection of deformation/rigidity theory, finite index subfactor theory, and geometric group theory, we prove the existence of a continuum of property (T) factors that are pairwise non-stably isomorphic and whose Jones index sets consist of all positive integers. These factors are realized as group von Neumann algebras associated with property (T) generalized wreath-like product groups introduced in [CIOS23b], where is abelian, is a non-parabolic subgroup of a relatively hyperbolic group with residually finite peripheral structure, and is a faithful action with infinite orbits. Integer index subfactors of are constructed from extensions of . This result advances an open question of P. de la Harpe [dlH95].
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Taxonomy
TopicsAdvanced Operator Algebra Research · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology
