Researcher Database

（Last updated : 2020-09-29 17:36:03）

AOI Hisashi

Department / Course College of Science and Engineering Department of Mathematical Sciences

Title / Position Associate Professor

Other Affiliations
1.	Graduate School of Science and Engineering
2.	Research Organization of Social Science (BKC) Research Center for Finance

Academic background
1.	～2000/03	Master Course │ Department of Mathematics │ Graduate School, Division of Natural Science │ Hokkaido University │ Completed
2.	～2003/03	Doctoral Program (2nd Semester) │ Department of Mathematics │ Graduate School, Division of Natural Science │ Hokkaido University │ Completed
3.		│ Hokkaido University M.S.
4.		│ Hokkaido University Ph.D. (Science)

Research activities
1.		Mathematical Society of Japan

Subject of research
1.	Study on actions of locally compact quantum groups on von Neumann algebras
2.	Study on relationships for operator algebras and dynamical system

Research summary
Analysis of Von Neumann algebra and action of quantum group, and a research on the dynamical system related with them By expanding action of matrix on the finite-dimensional vector space to bounded linear operators on the infinite Hilbert space, a variety of algebra structures consisting of operators can be assumed. Operator algebra theory started to analyze these structures. This theory that is developed originally based on quantum mechanics is not only an extension of linear algebras but also closely related with statistics such as free probability theory and is developing together with various fields. Among them, Von Neumann algebra that Murray-von Neumann started to research has been paid attention to as an interesting operator algebra characterized by both algebraic property and topological property. As one of the most prominent characteristics of Von Neumann algebra, it is closely related with the dynamic fields such as ergodic theory. The typical example is a Von Neumann algebra with a sub-algebra called Cartan sub-algebra (corresponding to diagonal matrix in matric algebra). The Von Neumann algebra like this can be characterized by the equivalence relation on the measure space. It has been clarified by the research so far that "Galois connection" exists that is a correspondence between a sub-algebra that contains Cartan sub-algebras and partial equivalence relation, the complementary operator related with it is characterized by 1cocycle on the equivalence relation, etc. At present, I am engaged in research on the operator of the quantum group of the Von Neumann algebra (which is an extension of general group operator) while I focus on these kinds of mutual relationships.

Present specialized field
Global Analysis (Keyword：von Neumann algebras , actions of locally compact quantum groups , Cartan subalgebras , ergodic theory)

Papers
1.	2014	The miR-17/106-p38 axis is a key regulator of the neurogenic-to-gliogenic transition in developing neural stem/progenitor cells │ Proc. Natl. Acad. Sci. USA │ 111 (4),pp.1604-1609 (Co-authored)
2.	2010	Hecke von Neumann algebra of ergodic discrete measured equivalence relations │ Publ. RIMS Kyoto Univ │ 46,pp.661–721 (Co-authored)
3.	2008	A characterization of a coaction reduced to that of a closed subgroup │ Tokyo J. Math. │ 30,pp.311–324 (Sole-authored)
4.	2008	A remark on the commensurability for inclusions of ergodic measured equivalence relations │ Hokkaido Math. J. │ 37,pp.545–560 (Sole-authored)
5.	2006	A characterization of coactions whose fixed-point algebras contain special maximal abelian -subalgebras │ Ergod. Th. and Dynam. Sys. │ 26,pp.1–33 (Co-authored)
Display All（8）