C*-Algebra Extensions and K-Homology. (AM-95), Volume 95 (eBook)

Ronald G. Douglas (Autor)

eBook Download: PDF

2016
96 Seiten
Princeton University Press (Verlag)
978-1-4008-8146-8 (ISBN)

Infos

Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Schlagworte: Addition • affine transformation • algebraic topology • Atiyah–Singer index theorem • automorphism • Banach Algebra • bijection • Boundary value problem • Bundle map • Calculation • C*-algebra • cardinal number • Category of abelian groups • Characteristic class • Chern class • Clifford Algebra • coefficient • cohomology • Compact operator • Completely positive map • Contact Geometry • continuous function • corollary • Diagram (category theory) • diffeomorphism • differentiable manifold • Differential operator • Dimension • Dimension function • Dimension (vector space) • Direct integral • Direct proof • Eigenvalues and Eigenvectors • equivalence class • equivalence relation • essential spectrum • Euler class • exact sequence • existential quantification • fiber bundle • finite group • Fredholm • Fredholm operator • free abelian group • Fundamental class • fundamental group • Hardy space • Hermann Weyl • hilbert space • Homological algebra • Homology (mathematics) • Homomorphism • Homotopy • Ideal (ring theory) • Inner automorphism • irreducible representation • K-group • K-theory • Lebesgue Space • Locally compact group • Maximal compact subgroup • Michael Atiyah • Monomorphism • Morphism • Natural number • Natural transformation • Normal Operator • Operator algebra • Operator norm • operator theory • orthogonal group • Pairing • Piecewise linear manifold • polynomial • Pontryagin class • Positive and negative parts • Positive map • pseudo-differential operator • quaternion • quotient algebra • Self-adjoint • Self-adjoint operator • Simply connected space • Smooth structure • Special case • Stein manifold • Strong topology • Subalgebra • SUBGROUP • Subset • Summation • tangent bundle • Theorem • Todd class • Topology • Torsion subgroup • Unitary Operator • Universal Coefficient Theorem • Variable (mathematics) • Von Neumann algebra
• ISBN-10: 1-4008-8146-3 / 1400881463
• ISBN-13: 978-1-4008-8146-8 / 9781400881468