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

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 metrizabl...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Douglas, Ronald G. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, NJ : Princeton University Press, [2016]
Colección:Annals of Mathematics Studies ; 95
Temas:
Algebra, Homological.
C*-algebras.
K-theory.
MATHEMATICS / Algebra / Linear.
Addition.
Affine transformation.
Algebraic topology.
Atiyah-Singer index theorem.
Automorphism.
Banach algebra.
Bijection.
Boundary value problem.
Bundle map.
C*-algebra.
Calculation.
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 (vector space).
Dimension function.
Dimension.
Direct integral.
Direct proof.
Eigenvalues and eigenvectors.
Equivalence class.
Equivalence relation.
Essential spectrum.
Euler class.
Exact sequence.
Existential quantification.
Fiber bundle.
Finite group.
Fredholm operator.
Fredholm.
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.
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 operator.
Self-adjoint.
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.
Acceso en línea:Texto completo
Texto completo
Descripción
Sumario: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.
Descripción Física:1 online resource (96 p.)
ISBN:9781400881468
9783110494914
9783110442496
Acceso:restricted access

Ejemplares similares