New methods of study in noncommutative algebraic geometry using representation theory of algebras

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400037
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Shizuoka University
• Principal Investigator: MORI IZURU 静岡大学, 理学部, 教授 (50436903)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 非可換代数幾何学 / 多元環の表現論 / AS-regular代数 / 量子射影空間

Outline of Final Research Achievements

Noncommutative algebraic geometry is a recently established research field, which studies algebras using tools from algebraic geometry. AS-regular algebras and quantum projective spaces are main objects of study in noncommutative algebraic geometry. The major achievement of this research project is that, by using tools not only from algebraic geometry, but also from representation theory of algebras, such as theory of n-representation infinite algebras, theory of superpotentials and theory of isolated singularities, we studied and classified AS-regular algebras and quantum projective spaces.

Free Research Field

数物系科学