Description: 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
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Title: Idempotent Matrices Over Complex Group Algebras By Ioannis Emmano
Weight: 539
EAN: 9783540279907
ISBN-10: 9783540279907
Date of Publication: 2005-10
Place of Publication: 2005-10
Book Series: Springer
Genre: MATHEMATICS / Algebra / General
Narrative Type: N/A
Features: N/A
Intended Audience: N/A
Ex Libris: No
Editor: N/A
Edition: N/A
Pagination: 296
Dimensions: 921x614
Number of Pages: 282 Pages
Publication Name: Idempotent Matrices over Complex Group Algebras
Language: English
Publisher: Springer-Verlag Berlin AND Heidelberg Gmbh & Co. KG
Item Height: 235 mm
Subject: Mathematics
Publication Year: 2005
Type: Textbook
Item Weight: 920 g
Author: Ioannis Emmanouil
Item Width: 155 mm
Series: Universitext
Format: Paperback
