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Algebra Lab
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The lab studies representations of quantum loop algebras and infinite-dimensional Lie algebras.
AboutAbout the lab
Studying how algebras act, through representations.
Prof. Kodera researches representation theory.
Representation theory is a field that studies how algebras act by translating them into concrete forms such as matrices.
The objects of study are representations of quantum loop algebras, Yangians, and related infinite-dimensional Lie algebras.
Crystal bases and quiver varieties are also listed as research areas.
Key terms
- Representation theory
- A field that studies how algebras act by translating them into matrices or transformations of vector spaces.
- Yangian
- A type of quantum group: an infinite-dimensional algebra that arose from the study of integrable systems.
- Quiver variety
- A space built from a diagram of points and arrows (a quiver). It allows representations of algebras to be captured in geometric form.
ResearchResearch themes
The specialty is representation theory.
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MembersFaculty
- Associate ProfessorRyosuke Kodera
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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: “Rubik's cube, CN II” kaʁstn Disk/Cat / CC BY-SA 3.0 (cropped)
- Representations of Quantum Groups and Infinite-Dimensional Lie Algebras: “E8 edgeoverlap” Tom Ruen (talk) / Public domain (cropped)
- Related lab (Fundamental Analysis Lab (Kazuki Hiroe)): “Riemann sphere” Jean-Christophe BENOIST / CC BY-SA 3.0 (cropped)
- Related lab (Algebra (Otsubo) Lab): “Ulam Spiral Divisors 100000” Cortexd / CC BY-SA 3.0 (cropped)
- Related lab (Algebra (Matsuda) Lab): “Abox - Sphere 4D 8K HQ OpenCL 20200323 klein” PantheraLeo1359531 / CC BY 4.0 (cropped)
- Related lab (Algebra Lab (Kenta Sato)): “Chatelet surface” Claudio Rocchini / CC BY-SA 3.0 (cropped)
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