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

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

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    Bog E-bog
    • Format
    • Bog, paperback
    • Engelsk

    Beskrivelse

    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.

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  • Vægt170 g
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    10 cm
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    15,2 cm
    22,9 cm

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    K-theory Operator theory Atiyah-Singer index theorem Topology Hilbert space Addition Banach-Algebra Chern class Clifford algebra Affine transformation Orthogonal group Hermann Weyl Boundary value problem Characteristic class Hardy space Stein manifold Polynomial Equivalence relation C-Algebra Eigenvalues and Eigenvectors Differentiable manifold Cohomology Normal Operator Theorem Diffeomorphism Homotopy Essential spectrum Self-adjoint operator Compact operator Unitary Operator Automorphism Cardinal number Homomorphism Von Neumann algebra Contact geometry Pseudo-Differential Operator Coefficient Irreducible Representation Dimension (vector space) Category of abelian groups Euler class Diagram (category theory) Dimension function Existential quantification Fundamental class equivalence class Fredholm Operator Exact Sequence Homology (mathematics) differential operator Direct integral Ideal (ring theory) Lebesgue Space Fundamental group Operator norm Operator algebra Natural transformation Pontryagin class Inner automorphism Piecewise linear manifold Smooth Structure summation Universal coefficient theorem Variable (mathematics) Monomorphism Maximal Compact Subgroup Quotient algebra Todd class Subalgebra Special case

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