Videolibrary
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
Video Library
Archive
Most viewed videos

Search
RSS
New in collection






The third Russian-Chinese conference on complex analysis, algebra, algebraic geometry and mathematical physics
May 14, 2016 12:10–12:50, Moscow, Steklov Mathematical Institute of RAS, Gubkina, 8
 


On the equations defining affine algebraic groups

V. L. Popov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Video records:
Flash Video 1,671.1 Mb
Flash Video 280.5 Mb
MP4 1,070.6 Mb

Number of views:
This page:532
Video files:114

V. L. Popov
Photo Gallery



Abstract: For the coordinate algebras of abelian varieties, the problem of finding a presentation by generators and relations canonically determined by the group structure has been explored and solved by D. Mumford. Since every connected algebraic group is an extension of a connected linear algebraic group by an abelian variety, the analogous problem for connected affine algebraic group naturally arises. The talk is intended to describing its solution based on solving two problems posed by D. E. Flath and J. Towber in 1992. From the standpoint of this theory, the usual naive presentation of $SL(n)$ as a hypersurface $\det=1$ in an $n^2$-dimensional affine space is adequate only for $n=2$: the canonical presentation defines $SL(3)$ as the intersection of 2 homogeneous and 2 inhomogeneous quadrics in a 12-dimensional affine space, $SL(4)$ as the intersection of 20 homogeneous and 3 inhomogeneous quadrics in a 28-dimensional affine space, etc.

Language: English
 
  Contact us:
 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024