DIAMANT Intercity Seminar on Lie Algebras

Friday 27 October 2006


All talks take place in the DIAMANT seminar room: 9.41 in the main building building (HG) at the TU/e in Eindhoven (map of campus, travel directions). Coffee is served in the adjacent DIAMANT lounge: 9.42.

10:30-11:00 arrival and coffee
11:00-12:00 Jan Draisma Classical theory of Lie algebras
This is a very concise review, for non-specialists, of some classical Lie algebra theory. We will touch on Sophus Lie's symmetries of ordinary differential equations and his transitive Lie algebras of vector fields on low-dimensional spaces, Cartan's classification of simple finite-dimensional complex Lie algebras, the Guillemin-Sternberg-Blattner theory of realising Lie algebras by means of vector fields, and their version of Cartan's classification of the infinite-dimensional primitive Lie algebras. In positive characteristic, the latter Lie-algebras have finite-dimensional truncated versions that are simple; these will appear in Strade's talk.
12:00-13:30 lunch break (lunch not included)
13:30-14:30 Erik Postma Lie algebras generated by extremal elements
Extremal elements play an important role in the classical Lie algebra theory, where they are known as long root elements. We will see that a finite set of extremal elements generates a finite-dimensional Lie algebra; this follows from a result of Zel'manov and Kostrikin. We study such Lie algebras where some pairs of generating elements are forced to commute and find cases where this construction produces the classical Lie algebras.
14:45-15:45 Helmut Strade On the classification of the simple Lie algebras
In this talk we report on the classification of the simple Lie algebras over algebraically closed fields. The classification in characteristic 0 is classical and goes back to Cartan; it will be recalled in Draisma's talk. In this talk, we will mainly deal with the modular case (over fields of positive characteristic). The relevant examples will be given, major methods will be explained and the final state of art will be presented.
16:00-17:00 Gábor Ivanyos Geometry of extremal elements
This talk, based on joint work with Arjeh Cohen, concerns characterization of simple Lie algebras generated by finitely many extremal elements using tools from geometry related to buildings. These algebras should be classical (with a very few exceptions) in arbitrary characteristic. The project is not finished yet, although we have shown that in many cases the point-line spaces of extremal elements in such Lie algebras are in fact isomorphic to shadow spaces of buildings of Dynkin type. The purpose of the talk is giving some insight into the classification of these spaces as well as an overview of the related open questions.
17:00 reception

Further information

There is no registration, and participation is free.