Idempotent Matrices over Complex Group Algebras

AvIoannis Emmanouil

Häftad, Engelska, 2005

Del i serien Universitext

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Beskrivning

The study of idempotent elements in group algebras (or, more generally, the study of classes in the K-theory of such algebras) originates from geometric and analytic considerations. For example, C.T.C. Wall [72] has shown that the problem of deciding whether a ?nitely dominated space with fundamental group? is homotopy equivalent to a ?nite CW-complex leads naturally to the study of a certain class in the reduced K-theoryK (Z?) of the group ringZ?. 0 As another example, consider a discrete groupG which acts freely, properly discontinuously, cocompactly and isometrically on a Riemannian manifold. Then, following A. Connes and H. Moscovici [16], the index of an invariant 0th-order elliptic pseudo-di?erential operator is de?ned as an element in the ? ? K -group of the reduced groupC -algebraCG. 0 r Theidempotentconjecture(alsoknownasthegeneralizedKadisonconjec- ? ? ture) asserts that the reduced groupC -algebraCG of a discrete torsion-free r groupG has no idempotents =0,1; this claim is known to be a consequence of a far-reaching conjecture of P. Baum and A. Connes [6].Alternatively, one mayapproachtheidempotentconjectureasanassertionabouttheconnect- ness of a non-commutative space;ifG is a discrete torsion-free abelian group ? thenCG is the algebra of continuous complex-valued functions on the dual r

Produktinformation

Utgivningsdatum:2005-10-20
Mått:155 x 235 x undefined mm
Format:Häftad
Språk:Engelska
Serie:Universitext
Antal sidor:282
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540279907

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

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)

Innehållsförteckning

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.