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.

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.

Autorentext

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.

Inhalt

Motivating Examples.- Reduction to Positive Characteristic.- A Homological Approach.- Completions of CG.