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Iyama Lab
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A lab in algebra that studies rings and their representations, and the structure of categories.
AboutAbout the lab
From representations of rings to the structure of categories.
The Iyama Lab studies ring theory and representation theory, both areas of algebra.
The lab works with rings such as quivers, orders, commutative rings, and dg categories, together with their representations.
The lab also studies the structure of categories associated with representations, such as derived categories, and their applications to cluster algebras and noncommutative resolutions of singularities.
Key terms
- Quiver
- A diagram made of points and arrows. It is used to represent rings and their representations in a visible form.
- Derived category
- A framework for handling objects such as modules by bundling them into sequences called complexes.
- Cluster algebra
- An algebra that arises from repeatedly exchanging variables one after another according to fixed rules.
ResearchResearch themes
The lab's research fields are algebra, ring theory, and representation theory, with the representation theory of orders as its theme. It studies rings and their representations, the structure of the associated categories, and applications of these.
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MembersFaculty
- ProfessorOsamu Iyama
VoicesStudent voices
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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: “Associaedre bleu” Kilom691 / CC BY-SA 4.0 (cropped)
- Representation Theory of Orders: “Dynkin diagram E8” Fropuff and Rogilbert / Public domain (cropped)
- Related lab (Abe Lab): “E8-with-thread” Jlrodri / CC BY-SA 3.0 (cropped)
- Related lab (Oshima Lab): “Weyl chambers for A2” Mathphysman / CC BY-SA 4.0 (cropped)
- Related lab (Kezuka Lab): “Addition on cubic” Jean Brette / CC BY 3.0 (cropped)
- Related lab (Takagi Lab): “CayleyCubic” Salix alba / CC BY-SA 3.0 (cropped)
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