Kyushu University Academic Staff Educational and Research Activities Database
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Toshihiko Masuda Last modified date:2023.11.28

Graduate School
Undergraduate School

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 Reseacher Profiling Tool Kyushu University Pure
Academic Degree
Ph. D. (Mathematical Sciences)
Country of degree conferring institution (Overseas)
Field of Specialization
operator algebra
Total Priod of education and research career in the foreign country
Outline Activities
My research field is the theory of operator algebras. In the theory of
operator algebras, we research subalgebras of bounded linear
operators on Hilbert spaces. There are two classes of operator algebras,
the class of C^*-algebras and that of von Neumann algebras. I mainly
study von Neumann algebras. My main interests are the theory of subfactors, and
automorphism groups and group actions on von Neumann
algebras. In subfactor theory, I analyze the construction introduced by
Longo and Rehren, and the structure of subfactors of type III_1. I
also study coactions of finite groups by using subfactor theory. Now I
try to apply this argument for study of actions of compact groups.
Research Interests
  • Research of outer actions of discrete groups on factors
    keyword : outer action
  • Research of one-parameter automorphism groups on factors
    keyword : one-parameter automorphism groups
  • Research of actions of compact groups on factors
    keyword : factor, compact group, action
    2005.04I study minimal actions of compact groups on factors with coauthor Dr. Tomatsu. We developed ultraproduct technique and proved the Rohlin type theorem and cohomology vanishing theorem. By intertwining argument, we classify outer coactions of compact groups on the injective factor of type II_1. Through duality theorem, we show the uniqueness of minimal actions. In type III case, it seems that we can classify actions by combining the above results and structure theorem of type III factors. So we are now studying along this idea..
  • Group actions on subfactors
    keyword : subfactor, group action
    1997.04~2004.04I studied group actions on subfactors. I introduced cohomological invariants, and classified actions by these invariants under some nice conditions..
Academic Activities
1. Masuda Toshihiko, Tomita-Takesaki theory and its application to the structure theory of factors of type III, Mathematical Journal of Okayama University, 10.18926/mjou/56009, Vol.60, No.1, pp.37-58, 2018.01, We give a survey of Tomita-Takesaki theory and the development of analysis of structure of type III factors, which started from Tomita-Takesaki theory..
1. 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, 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.
2. Toshihiko Masuda, Reiji Tomatsu, Classification of actions of discrete Kac algebras on injective factors, Memoirs of American Mathematical Society, DOI:, 245, 1160, 2016.07, 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..
3. Toshihiko Masuda, Reiji Tomatsu, Rohlin flows on von Neumann algebras, Memoirs of American Mathematical Society, DOI:, 244, 1153, 2016.06, 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..
4. 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.
5. 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.
6. 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.
7. 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.
Educational Activities
In 2010, I give the lecture of linear algebra for undergraduated students,
that of functional analysis for graduated students of mathematics,
that of Fourier analysis for students in the course of technology. In the
lecture of linear algebra, I first teach the solution of linear equations, computations of determinants.
Then I teach the theory of abstract linear algebra.
In the lecture of functional analysis, I taught general theory of Hibert spaces and spectral decomposition of compact
In the lecture of Fourier analysis, I teach the computations and applications to differential equations