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Nakanishi Lab
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An algebra lab that studies cluster algebras and infinite-dimensional integrable systems.
AboutAbout the lab
Exploring the algebraic structure known as cluster algebras
Professor Tomoki Nakanishi's lab studies the algebraic structures called cluster algebras.
Cluster algebras are a class of commutative algebras introduced around 2000, and they generalize the commutative algebras that appear in Lie theory.
They can be regarded as a kind of extension of root system theory, and they are being actively studied as algebraic and combinatorial structures that appear in many areas of mathematics.
In the graduate school's list of research fields, the lab is classified under representation theory, infinite-dimensional integrable systems, and mathematical physics.
Key terms
- Cluster algebra
- A class of algebras that generalizes the commutative algebras of Lie theory. Prototypes include the coordinate rings of Grassmannians.
- Cluster scattering diagram
- A framework that reformulates cluster algebras using diagrams.
ResearchResearch themes
The lab studies the foundations and applications of cluster algebras. Cluster algebras are regarded as an extension of root system theory and as algebraic and combinatorial structures that appear in many areas of mathematics.
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MembersFaculty
- ProfessorTomoki Nakanishi
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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: “Root system A2 with labels” Mark L MacDonald; derivative of work of User:Smithers888 and User:Maksim / CC BY-SA 3.0 (cropped)
- Cluster algebras and cluster scattering diagrams: “Algebraic-structures” Marco Piedra / CC BY-SA 3.0 (cropped)
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