arXiv subjects
Publications and source records attributed to Toshihiko Masuda.
Gelaki-Naidu-Nikshych and Turaev-Virelizier showed the existence of $G$-braiding on the relative Drinfeld center of a $G$-graded tensor category. We will explain this concept from the viewpoint of Longo-Rehren inclusions.
We apply Evans-Kishimoto's intertwining argument to the classification of actions of discrete amenable groups into the normalizer of a full group of an ergodic transformation. Our proof does not depend on the types of ergodic transformations.
We classify outer actions (or $\mathscr{G}$-kernels) of discrete amenable groupoids on injective factors. Our method based on unified approach for classification of discrete amenable groups actions, and cohomology reduction theorem of discrete amenable equivalence relations. We do not use Katayama-Takesaki type resolution group approach.
We show the relative bicentralizer flow and the relative flow of weights are isomorphic for an inclusion of injective factors of type III$_1$ with finite index, or an irreducible discrete inclusion whose small algebra is an injective factor of type III$_1$.
In this paper, we generalize Izumi's result on uniqueness of realization of finite C$^*$-tensor categories in the endomorphism category of the injective factor of type II_1 for finitely generated strongly amenable C$^*$-tensor categories by applying Popa's classification theorem of strongly amenable subfactors of type III_1.
We will study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. We will construct a new invariant which generalizes a characteristic invariant for a discrete group action, and we will present a complete classification. The second is a centrally free action. By constructing a Rohlin tower in an asymptotic centralizer, we will show that the Connes-Takesaki module is a complete invariant.
We present a simple sufficient condition for triviality of obstruction in the orbifold construction. As an application, we can show the existence of subfactors with principal graph $D_{2n}$ without full use of Ocneanu's paragroup theory.
We will introduce the Rohlin property for flows on von Neumann algebras and classify them up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on the injective type II$_1$ factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III$_0$ factors. Several concrete examples are also studied.
We present a simple unified proof of classification of discrete amenable group actions on injective factors. Our argument does not depend on types of factors. We also show the second cohomology vanishing theorem for arbitrary cocycle crossed actions of discrete amenable groups on the injective factor of type II$_1$.
We classify a certain class of minimal actions of a compact Kac algebra with amenable dual on injective factors of type III. Our main technical tools are the structural analysis of type III factors and the theory of canonical extension of endomorphisms introduced by Izumi.
We introduce the notions of approximate innerness and central triviality for endomorphisms on separable von Neumann factors, and we characterize them for hyperfinite factors by Connes-Takesaki modules of endomorphisms and modular endomorphisms which are introduced by Izumi. Our result is a generalization of the corresponding result obtained by Kawahigashi-Sutherland-Takesaki in automorphism case.
We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II$_1$. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.
We apply the Evans-Kishimoto type argument for centrally free actions of discrete amenable groups on McDuff factors, and classify them. Especially, we present a different proof that the Connes-Takesaki modules are complete cocycle conjugacy invariants for centrally free actions of discrete amenable groups on injective factors.
We construct approximately inner actions of discrete amenable groups on strongly amenable subfactors of type II_1 with given invariants, and obtain classification results under some conditions. We also study the lifting of the relative χgroup.
Using the continuous decomposition, we classify strongly free actions of discrete amenable groups on strongly amenable subfactors of type III$_λ, 0 < λ< 1$. Winsløw's fundamental homomorphism is a complete invariant. This removes the extra assumptions in the classification theorems of Loi and Winsløw and gives a complete classification up to cocycle conjugacy.