Alberto Ibort, Miguel A. Rodriguez
May 15, 2019 Forthcoming
Reference - 250 Pages
ISBN 9781138035867 - CAT# K31765
For Instructors Request Inspection Copy
A. Connes claimed that “mathematicians denied groupoids its proper status just because the pejorative suffix –id,” but they are the relevant structures behind many notions in mathematics and physics. This book provides an elementary introduction to the theory of groupoids and their representations, encompassing the standard theory of groups with plenty of examples and applications ranging from combinatorics to the topology of graphs.
Finite groups and groupoids: definitions and examples. The categorical language: the “right” definition of groups and groupoids. Graphs and groupoids. A wealth of applications: from topology to databases. The structure of finite groupoids (and groups): subgroupoids and quotients. Linear representations of groups and groupoids: basic definitions and examples. The groupoid algebra: the operator approach. Characters and representations: examples and applications. Products and reduction of representations.