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June 14, 2016 15:00, International Workshop "Hopf Algebras, Algebraic Groups and Related Structures", June 13-17, 2016, Memorial University of Newfoundland, St John's, NL, Canada
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Coordinate algebras of connected affine algebraic groups: generators and relations
V. L. Popov Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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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 in 1966. 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
Website:
https://www.mun.ca/aac/Workshops/NextWork/AAC_2016_HAAG16.pdf
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