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E‐Theory is a Special Case of KK‐Theory
Author(s) -
Manuilov V.,
Thomsen K.
Publication year - 2004
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611503014436
Subject(s) - mathematics , separable space , homomorphism , hilbert space , unital , homotopy , mathematics subject classification , pure mathematics , algebra over a field , discrete mathematics , combinatorics , mathematical analysis
Let A and B be C*‐algebras, with A separable and B σ‐unital and stable. It is shown that there are natural isomorphisms E ( A , B ) = K K ( S A , Q ( B ) ) = [ S A , Q ( B ) ⊗ K ] , where SA = C 0 (0, 1) ⊗ A , […, …] denotes the set of homotopy classes of *‐homomorphisms, Q ( B ) = M ( B ) / B is the generalized Calkin algebra, and K denotes the C*‐algebra of compact operators of an infinite‐dimensional separable Hilbert space. 2000 Mathematics Subject Classification 19K35, 19K33, 46M15.