Study on infinite dimensional algebraic groups and Lie algebras, and application to quasi-periodic and aperiodic structures

2022 Fiscal Year Final Research Report

• Project/Area Number: 17K05158
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: University of Tsukuba
• Principal Investigator: Morita Jun 筑波大学, 数理物質系(名誉教授), 名誉教授 (20166416)
• Project Period (FY): 2017-04-01 – 2023-03-31
• Keywords: 代数群 / リー代数 / 代数的K理論 / 局所アフィン・リー代数 / カッツ・ムーディ群 / スキーム / 四元数体 / 量子ビット

Outline of Final Research Achievements

(1)The structure of K_2SL_2(R) was determined for several prime numbers p_1,...,p_n, where R = [1/p_1,...,1/p_n]. (2) We classified minimal locally affine Lie algebras. This is a joint work with Yoji Yoshii. (3) We characterized affine Kac-Moody groups using schemes and Galois descert. This is a joint work with A. Pianzola and T. Shibata. (4) We discussed some infinite root system obtained from H4 root systems in quaternion division ring, and obtained a new application to quantum bits. This is a joint work with Robert Moody.

Free Research Field

代数学

Academic Significance and Societal Importance of the Research Achievements

何れも有限次元および無限次元の代数群とリー代数に関わる基本的な研究成果である。新たな知見も多く含み、数学的な価値は高く、意義深いと認めとられる。