Algebraic groups generated by semisimple elements

Thời gian: 9h30-11h00, thứ Năm, 29/10

Địa điểm: Phòng 512 nhà A6, Viện toán học

Abstract: It is known that a linear algebraic group G is generated by unipotent elements if and only if G is a semidirect product of a semisimple group and the unipotent radical. In this talk, we describe linear algebraic groups generated by semisimple elements. We also discuss what minimal number of factors is needed to represent each element of a given group as a product of unipotent/semisimple elements, and how many one-dimensional unipotent/multiplicative subgroups are required to generate a given group.

If time permits, we will come to the possible passage from linear algebraic groups to the groups of automorphisms of affine algebraic varieties. This work is prepared within the framework of the project “International Academic Cooperation” HSE University.