Bounded elementary generation of Chevalley groups

• 主讲人：Prof. Nikolai Vavilov
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2022-06-16 20:00 - 2022-06-16 21:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/003A36414D9928A3A199EFE5BE0DF5E0
Valid Until: 2026-07-31 23:59

 

Abstract: We discuss several results on bounded elementary generation and bounded commutator width for Chevalley groups over Dedekind rings of arithmetic type in positive characteristics. In particular, Chevalley groups of rank \ge 2 over polynomial rings F_q[t] and Chevalley groups of rank \ge 1 over Laurent polynomial F_q[t,t^{-1}] rings, where F_q is a finite field of q elements, are boundedly elementarily generated. We sketch several proofs, using reciprocity laws, symbols in algebraic K-theory, and surjective stability for K-functors. As a result, we establish rather plausible explicit bounds, that do not depend on q and are better than the known ones even in the number case. Using these bounds we can also produce sharp bounds of the commutator width of these groups. We also mention several applications (Kac---Moody groups, first order rigidity, etc.) and possible generalisations. This is joint work with Boris Kunyavskii and Eugene Plotkin.

 

Bio: Professor Nikolai Alexandrovich Vavilov works at Saint-Petersburg State University, Department of Mathematics and Computer Sciences (he was one of the co-founders of the Department) and at Saint Petersburg Department of Steklov Mathematical Institute. He is one of the best Russian algebraists having a big number of brilliant results in Structure theory and representations of algebraic groups, algebraic K-theory, overgroups of semisimple groups and tori. Prof. Vavilov graduated from Leningrad State University (now Saint Petersburg State University) and got his Doctor Degree (habilitation) in 1988. He has got a big number of prestigious awards and prizes and grew up dozens of students.

Besides, Nikolai Alexandrovich intensively cooperates with Chinese colleagues. He is one of those people who launched the current program of Russian - Chinese collaboration.