Basic Lie Theory
To Gerhard Hochschild
Preface and Acknowledgments
Groups and Lie Algebras; Introduction
Topological Groups . . . . . . . . . . . . . .
Lie Groups .
Introduction to Lie Groups and Lie Algebras Alexander Kirillov, Jr.
Department of Mathematics, SUNY at Stony Brook, Stony Brook, NY 11794, USA E-mail address: [email protected] URL: http:/www.math.sunysb.edu/~kirillov
Chapter 1. Introducti
All metrics have curvature tensors characterised
by its invariants as a limit: the -property.
arXiv:1107.3210v1 [gr-qc] 16 Jul 2011
Faculty of Science and Technology,
University of Stavanger,
N-4036 Stavanger, Norway
Linearly Dependent Sets of Algebraic
Curvature Tensors with a Nondegenerate Inner
Research Experience for Undergraduates
California State University San Bernardino
San Bernardino, California 92407
August 19, 2011
GROUP ACTIONS ON SETS
1. Group Actions
Let X be a set and let G be a group. As before, we say that G acts on X if we have a representation
: G S (X ) or equivalently there is a binary operation G X X satisfying the rules
1x = x
for all x X,