Subfactors associated to compact Kac algebras

TL;DR

This paper constructs and analyzes subfactors arising from actions of compact Kac quantum groups on inclusions of finite-dimensional C*-algebras and II_1 factors, providing explicit invariants and broad applications.

Contribution

It introduces a method to construct subfactors from compact Kac quantum group actions and computes their invariants, extending previous frameworks to new classes of quantum symmetries.

Findings

Explicit subfactor constructions from compact Kac quantum groups.

Computation of Jones index and standard invariant for these subfactors.

Applications to subgroups, projective representations, quantum groups, and models.

Abstract

We construct inclusions of the form $(B_0\otimes P)^G\subset (B_1\otimes P)^G$, where $G$ is a compact quantum group of Kac type acting on an inclusion of finite dimensional $\c^*$-algebras $B_0\subset B_1$ and on a $II_1$ factor $P$. Under suitable assumptions on the actions of $G$, this is a subfactor, whose Jones to er and standard invariant can be computed by using techniques of A. Wassermann. The subfactors associated to subgroups of compact groups, to projective representations of compact groups, to finite quantum groups, to finitely generated discrete groups, to vertex models and to spin models are of this form.