Symmetric Spaces of Noncompact type

Martin Moskowitz

Authors

Martin Moskowitz Department of Mathematics, CUNY Graduate Center 365 Fifth Ave. New York NY 10016. USA.

Keywords:

Semisimple Lie group and Lie algebra of non-compact type, Maximal compact subgroup and maximal subalgebra of compact type and their conjugacy. Cartan and polar decomposition, rank, irreducible symmetric space, isometry group, Killing form, exponential map, Cartan involution, law of cosines, two point homogeneous space

Abstract

This article gives a detailed introduction to symmetric spaces of non-compact type and their relation to corresponding semisimple lie groups. This is done more or less from scratch and explicitely without the reader having to know large parts of modern differential geometry