Vorträge im Schwerpunkt Reelle Geometrie und Algebra
Freitag, 11. Juni 2010, um 14:15 Uhr in F426 (Oberseminar)
Mikhail Kotchetov (Memorial
University, St. John's)
Group gradings on simple
Lie algebras
We are interested in describing all group gradings on simple
Lie algebras over an algebraically closed field F, i.e., all
vector space decompositions of the form L =⊕g∈G
Lg
where L is a simple Lie algebra, G is a group,
and [Lg, Lh]⊂
Lgh
for all g,h∈G. In the case char F = 0, all gradings on
the classical simple
Lie algebras of the series A, B, C, D and on some exceptional simple
Lie algebras have been classified as a result of efforts of
many authors. Y. Bahturin, S. Mongomery and myself showed that,
essentially, the same
classification is valid for the Lie algebras A, B, C, D in the
case char F = p > 2. Another important class of simple
finite-dimensional Lie algebras in
positive characteristic is the Lie algebras of Cartan type: Witt,
special, Hamiltonian and contact. (Similar algebras exist in zero
characteristic, but they are
infinite-dimensional.) Y. Bahturin, J. McGraw and myself have recently
made progress in the classification of gradings on Lie algebras of
Cartan type.
The talk will be an overview of the classification results mentioned
above.
zuletzt
geändert am 20. April 2010
