
School of Mathematics and Statistics
Arjeh Cohen
Technische Universiteit Eindhoven
Extremal elements in Lie algebra.
Friday 24th November, 121pm, Carslaw 275.
We shall discuss Lie algebras L generated by extremal
elements, that is elements x such that
[x,[x,L]] \subseteq <x>. Any Lie algebra
generated by a finite number of extremal elements is finite
dimensional. The minimal number of extremal generators for the
complex simple Lie algebras of type A_{n}
(n>0), B_{n} (n>2),
C_{n} (n>1), D_{n}
(n>3), E_{n} (n=6,7,8),
F_{4} and G_{2} are n+1,
n+1, 2n, n, 5, 5, and 4 in the respective
cases. There is an elegant structure theory for the Lie algebras
under study, and there are connections with Tits geometry, notably
Timmesfeld's classification of groups generated by abstract root
groups.
