Abstract : I will describe all maximal locally solvable subalgebras of gl(\infty) in terms of generalized flags. It turns out, that they are not necessarily unions of Borel subalgebras of gl(n), for any presentation of gl(\infty) as the union of gl(n). I will also present some interesting examples.
Abstract : In this talk, the classification of all irreducible weight modules with finite dimensional weight spaces over higher rank Virasoro algebras $Vir[G]$ (of rank $n$) will be given. There are two different classes of them. One class is formed by simple modules of intermediate series (whose weight spaces are all $1$-dimensional), the other class consists of weight modules $V$ (induced from intermediate series modules over a subalgebra which is a rank $n-1$ Virasoro algebra) whose weight spaces are not uniformly bounded and whose weight sets are, roughly speaking, half of the set $\Lambda_0+G$, where $\Lambda_0\in C$ can be chosen as a weight of $V$. The result for $n=1$ was proved by O. Mathieu with completely different method.
Abstract : Loop algebras were introduced by V. Kac to provide concrete realizations of affine Kac-Moody Lie algebras. I will review his construction, give a new proof of his main result (using Galois cohomology), and explain how these ideas can be used in the classification of loop algebras of arbitrary algebras. We will illustrate this new approach in the case of simple finite dimensional Lie superalgebras.
All talks will be in the Department of Mathematics and Statistics of the University of Ottawa, 585 King Edward (KED on the campus map), room B15.
Financial support for participating graduate students and postdoctoral fellows is available. If you are interested please contact Erhard Neher (firstname.lastname@example.org) as soon as possible, but definitely before December 5, and ask your supervisor to do the same.