Chevalley groups over rings of polynomials

• 主讲人：Dr. Anastasia Stavrova (Saint Petersburg State University)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2022-06-02 21:00 - 2022-06-02 22:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/F98451EB7316CD31517990FA148AC092
Valid Until: 2026-07-31 23:59

 

Abstract: Let D be a Dedekind domain. In 1977, A. Suslin established that for any N>=3, and any n>=1, one has SL_N(D[x_1,...,x_n])=SL_N(D)E_N(D[x_1,...,x_n]), where E_N(D[x_1,...,x_n]) is the elementary subgroup of SL_N(D[x_1,...,x_n]), i.e. the subgroup generated by the unipotent elementary transformation matrices E+tE_ij, where E is the unit matrix, E_ij is the matrix with 1 at the position i,j and 0 everywhere else, and t is an arbitrary element of the polynomial ring D[x_1,...,x_n]. In particular, this implies that SL_N(Z[x_1,...,x_n])=E_N(Z[x_1,...,x_n]), where Z is the ring of integers. We discuss an extension of this result to all split simple linear algebraic groups (also called Chevalley groups) and to regular rings D of higher dimension.

 

Bio: Dr. Anastasia Stavrova is an expert in algebraic groups, non-associative algebra, and algebraic K-theory. She is a researcher in the Chebyshev Laboratory and Department of Mathematics and Computer Science at Saint Petersburg State University. Dr. Stavrova earned a specialist degree in mathematics at Saint Petersburg State University in 2005 and got her PhD in 2009 supervised by Nikolai Vavilov. She has had a great experience working overseas (the University of Leiden, University of Padua, Ludwig Maximilian University of Munich, and the University of Duisburg-Essen). Also, she was Jerrold E. Marsden Postdoctoral Fellow at the Fields Institute in Canada. Anastasia Stavrova obtained a great number of brilliant results in Algebra and related areas. She won the Young Mathematician Prize of the Saint Petersburg Mathematical Society in 2009, and the Young Russian Mathematics Scholarship in 2016. In 2018, she has got the G. de B. Robinson Award from the Canadian Mathematical Society.