Sydney University Algebra Seminar

    University of Sydney

    School of Mathematics and Statistics

    Algebra Seminar

    Arjeh Cohen
    Technische Universiteit Eindhoven

    Extremal elements in Lie algebra.

    Friday 24th November, 12-1pm, 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 An (n>0), Bn (n>2), Cn (n>1), Dn (n>3), En (n=6,7,8), F4 and G2 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.