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.
Author(s): Ioannis Emmanouil
Series: Universitext
Edition: 1
Publisher: Springer
Year: 2005
Language: English
Pages: 288
Cover......Page 1
Idempotent Matrices over
Complex Group Algebras......Page 3
ISBN-10 3540279903......Page 4
Preface......Page 6
Contents......Page 9
1
Introduction......Page 12
2
Motivating Examples......Page 60
3
Reduction to Positive Characteristic......Page 84
4
A Homological Approach......Page 121
5
Completions of CG......Page 168
A
Tools from Commutative Algebra......Page 216
B
Discrete Ring-Valued Integrals......Page 236
C
Frobenius’ Density Theorem......Page 244
D
Homological Techniques......Page 248
E
Comparison of Projections......Page 271
References......Page 279
Index......Page 283
Universitext......Page 285
