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Arano Lab
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Research on quantum groups over noncommutative spaces, studied through operator algebras.
AboutAbout the lab
Studying groups on noncommutative spaces
Prof. Arano studies operator algebras and, from that standpoint, quantum groups.
An operator algebra can be thought of as a "noncommutative version" of the algebra formed by continuous functions on a space.
Studying the group structure on such a "noncommutative space" is quantum group theory in the sense of operator algebras.
Centered on the representation theory and topological aspects of quantum groups, the professor also works on the classification of group actions and on tensor categories.
Key terms
- Operator algebra
- A collection of bounded linear operators on a Hilbert space, equipped with addition and multiplication.
- Quantum group
- A generalization of the notion of a group to "noncommutative spaces." An important concrete example in operator algebra theory.
- Tensor category
- A category equipped with an operation for "multiplying" objects together. It generalizes the structure of the collection of all representations of a group.
- Subfactor theory
- A theory that studies the relationship between an operator algebra and an operator algebra contained in it. It has aspects resembling Galois theory.
ResearchResearch themes
From the viewpoint of operator algebras, the lab studies quantum groups, which are group structures on "noncommutative spaces." Quantum group theory is an important source of concrete examples in operator algebras, and is also related to subfactor theory, which is the analogue of Galois theory in operator algebra theory.
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MembersFaculty
- Associate ProfessorYuki Arano
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Mathematics lecture notes, Mathematical analysis, Linear algebra, Rostov-on-Don, Russia” Vyacheslav Argenberg / CC BY 4.0 (cropped)
- Representation theory of quantum groups and classification of actions: “A4 Cayley graph” נוצר על ידי משתמש:עוזי ו. / CC BY-SA 3.0 (cropped)
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