Idempotent Matrices over Complex Group Algebras

by Ioannis Emmanouil

Overview

The theory of idempotent matrices with entries in complex group algebras has recently experienced a revival, in view of its close relationship with deep geometric problems and conjectures. The relevant questions studied in this book for general groups are motivated by specific examples. A variety of techniques is employed from commutative algebra, homological algebra and functional analysis. The book can serve as an introduction to this lively research area. The pace is suitable for independent study and the level of the presentation not very demanding. The exercises at the end of each chapter form an essential part of the book.

Product Details

ISBN-13:	9783540279907
Publisher:	Springer Berlin Heidelberg
Publication date:	12/01/2005
Series:	Universitext
Edition description:	2006
Pages:	282
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

About the Author

Ioannis Emmanouil was initiated to mathematics in Athens, Greece and then moved to Berkeley, where he studied homological algebra, algebraic geometry and K-theory with Mariusz Wodzicki. After receiving his Ph.D. from Berkeley in 1994, he taught for three years at the University of Michigan as a Hildebrandt Assistant Professor. He moved back to Europe in 1997 and after a year at IHES, returned to Greece in 1998. At present, he is a member of the faculty of the University of Athens.

Table of Contents

Introduction.- Motivating Examples.- Reduction to Positive Characteristic.- A Homological Approach.- Completions of CG.- Appendices: Tools from Commutative Algebra.- Discrete Ring-valued Integrals.- Frobenius' Density Theorem.- Homological Techniques.- Comparison of Projections.

Editorial Reviews

From the reviews:

"The study of idempotent elements in the group algebras originates from geometric and analytic considerations. … This book provides an introduction to the study of these problems for graduate students and researchers … . collects and presents in a systematic way basic techniques and important results that have been obtained during the past few decades. … The book is suitable for independent study … . Moreover, all chapters and appendices finish with a sufficient number of exercises that also increase the quality of the book." (S. V. Mihovski, Zentralblatt MATH, Vol. 1093 (19), 2006)

From the Publisher