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Itaba Lab
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The lab explores the connection between the representation theory of algebras and noncommutative algebraic geometry.
AboutAbout the lab
Toward links between representation theory and noncommutative algebraic geometry
The Itaba Lab studies the representation theory of algebras and noncommutative algebraic geometry, both within the field of algebra.
The Hochschild cohomology of an algebra is an invariant of Morita equivalence, stable equivalence of Morita type, and derived equivalence of algebras, and it is also an object of interest from the standpoint of the representation theory of algebras.
Noncommutative algebraic geometry began with the classification of 3-dimensional AS-regular algebras, which are the coordinate rings of quantum projective planes.
Noting that noncommutative algebraic geometry and the representation theory of algebras are closely related, the lab aims to investigate the connection between them.
Key terms
- Hochschild cohomology
- A quantity defined for an algebra, and one of the invariants of Morita equivalence, stable equivalence of Morita type, and derived equivalence of algebras
- AS-regular algebra
- A type of algebra studied in noncommutative algebraic geometry. The 3-dimensional ones correspond to the coordinate rings of quantum projective planes
ResearchResearch themes
The Itaba Lab studies the representation theory of algebras and noncommutative algebraic geometry, both within the field of algebra. Noting that the two fields are closely related, the lab aims to investigate the connection between them.
View More ↗MembersFaculty
- Associate ProfessorAyako Itaba
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