Concept
Semi-simplicity
Publications associées (31)
Linear Algebraic Groups and Finite Groups of Lie Type
Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisim ...
Cambridge University Press2011Chaplygin systems associated to Cartan decompositions of semi-simple Lie groups
We relate a Chaplygin type system to a Cartan decomposition of a real semi-simple Lie group. The resulting system is described in terms of the structure theory associated to the Cartan decomposition. It is shown to possess a preserved measure and when inte ...
Elsevier2010On the bounded cohomology of semi-simple groups, S-arithmetic groups and products
We prove vanishing results for Lie groups and algebraic groups (over any local field) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups. Related rigidity results are established for S-arithmetic groups and gr ...
De Gruyter2010Nilpotent subalgebras of semisimple Lie algebras
Let g be the Lie algebra of a semisimple linear algebraic group. Under mild conditions on the characteristic of the underlying field, one can show that any subalgebra of g consisting of nilpotent elements is contained in some Borel subalgebra. In this Note ...
2009