九州大学-研究者情報 [増田俊彦 (教授) 数理学研究院解析部門]

増田俊彦（ますだとしひこ）

データ更新日：2024.04.17

教授　／　数理学研究院解析部門

原著論文

1.	Toshihiko Masuda, Actions of discrete amenable groups into the normalizers of full groups of ergodic transformations, Ergodic theory and Dynamical Systems, 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..
2.	Toshihiko Masuda, Classification of outer actions of discrete amenable groupoids on injective factors, Journal of Mathematical Society of Japan, DOI: 10.2969/jmsj/86328632, 74, 3, 873-901, 2022.07, 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..
3.	Toshihiko Masuda, On the relative bicentralizer flows and the relative flow of weights of inclusions of factors of type III, Publications of the Research Institute for Mathematical Sciences, 10.4171/PRIMS/56-2-4, 56, 2, 391-400, 2020.01, [URL], We show that the relative bicentralizer ow and the relative ow of weights are isomorphic for an inclusion of injective factors of type III₁ with Inite index, or an irreducible discrete inclusion whose small algebra is an injective factor of type III.
4.	Toshihiko Masuda, Classification of Roberts actions of strongly amenable C--tensor categories on the injective factor of type III1, INTERNATIONAL JOURNAL OF MATHEMATICS*, 10.1142/S0129167X17500525, 28, 7, 2017.06, In this paper, we generalize Izumi's result on uniqueness of realization of nite C∗-tensor categories in the endomorphism category of the injective factor of type III1 for nitely generated strongly amenable C∗-tensor categories by applying Popa's classication theorem of strongly amenable subfactors of type III1..
5.	Toshihiko Masuda, A simple sufficient condition for triviality of obstructions in the orbifold construction for subfactors, Mathematica Scandinavica, 10.7146/math.scand.a-26240, 121, 1, 101-110, 2017.04, [URL], We present a simple sufficient condition for triviality of obstructions 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..
6.	Toshihiko Masuda, Reiji Tomatsu, Classification of actions of discrete Kac algebras on injective factors, Memoirs of American Mathematical Society, DOI: http://dx.doi.org/10.1090/memo/1160, 245, 1160, 2016.07, [URL], 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..
7.	Toshihiko Masuda, Reiji Tomatsu, Rohlin flows on von Neumann algebras, Memoirs of American Mathematical Society, DOI: http://dx.doi.org/10.1090/memo/1153, 244, 1153, 2016.06, [URL], We will classify Rohlin flows on von Neumann algebras 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 II1 factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III0 factors. Several concrete examples are also studied..
8.	増田俊彦, Unified approach to classification of actions of discrete amenable groups on injective factors, Journal für die reine und angewandte Mathematik, 10.1515/crelle-2011-0011, 683, 1-47, 2013.10, We present a simple unified proof of the classification of discrete amenable group actions on injective factors. Our argument does not depend on the types of factors, and is based on the technique of Evans and Kishimoto..
9.	Toshihiko Masuda and Reiji Tomatsu, Classification of minimal actions of a compact Kac algebra with amenable dual on injective factors of type III, Journal of Functional Analysis, 258, 1965--2025, 2010.01.
10.	Toshihiko Masuda, Reiji Tomatsu, Approximate innerness and central triviality of endomorphisms, Advance in Mathematics, 220巻　1075--1134, 2009.01.
11.	Toshihiko Masuda, Classification of actions of duals of finite groups on the AFD factor of type II_1, Journal of Operator theory, 60巻273--300, 2008.10.
12.	Toshihiko Masuda, Evans-Kishimoto type argument for actions of discrete amenable groups on McDuff factors, Mathematica Scandianvica, Vol 101, pp48--64., 2007.10.
13.	Toshihiko Masuda, Reiji Tomatsu, Classification of minimal actions of a compact Kac algebra with amenable dual, Commucations in Mathematical Physics, Vol 274, pp 487--551, 2007.09.
14.	Toshihiko Masuda, An analogue of Connes-Haagerup approach for classification of subfactors of type III_1, Journal of Mathematical Society of Japan, 10.2969/jmsj/1150287301, 57, 4, 959-1001, Vol. 57 959--1003, 2005.01.
15.	Toshihiko Masuda, Classification of approximately inner actions of discrete amenable groups on strongly amenable subfactors, International Journal of Mathematics, 10.1142/S0129167X05003296, 16, 10, 1193-1206, Vol. 16, 1193--1206, 2005.01.
16.	MASUDA, Toshihiko, On non-strongly free automorphisms of subfactors of type III_0, Canadian Mathematical Bulletin, Vol.46, 419--428, 2003.01.
17.	MASUDA, Toshihiko, Notes on group actions on subfactors, Journal of Mathematical Society of Japan, Vol. 55, 1--11, 2003.01.
18.	MASUDA, Toshihiko, Extension of automorphisms of a subfactor to the symmetric enveloping algebra, International Journal of Mathematics, Vol.12, 637--659, 2001.01.
19.	MASUDA, Toshihiko, Generalization of Longo-Rehren construction to subfactors of infinite depth and amenability of fusion algebras, Journal of Funcitional Analysis, Vol. 171巻, 53--77, 2000.01.
20.	Masuda, Toshihiko, Classification of actions of discrete amenable groups on subfactors of type III_\lambda, Proceedings of American Mathematical Society, Vol 127, 2053--2057, 1999.07.
21.	Masuda, Toshihiko, Classification of strongly free actions of discrete amenable actions on subfactors of type III_0, Pacific Journal of Mathematics, Vol 191, 347--357, 1999.01.
22.	Masuda, Toshihiko, An analogue of Longo's canonical endomorphism in bimodule theory and its application to asymptotic inclusions, International Journal of Mathematics, Vol. 8, 249--264, 1999.01.
23.	Toshihiko Masuda, Classification of outer actions of discrete amenable groupoids on injective factors, Journal of Mathematical Society of Japan, 掲載決定, 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..

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