Date:	Fri, April 25, 2014
Time:	13:45
Place:	Seminar Room (120), Research I

Abstract: The classical semisimple Lie groups are a relevant set of examples in the study of the structure of general semisimple Lie groups. The polar decomposition of matrices and the QR-decomposition are a first set of results that emphasise the importance of a certain compact subgroup of matrices in understanding the topology of the initial Lie group. In this talk I will describe two generalisations of this results, namely the Cartan decomposition and the Iwasawa decomposition and explain the role that compact real forms and restricted roots have into this constructions. The talk will end with topological consequences and symmetric spaces.