TY - JOUR

T1 - Algebraic K-theory of stable C*-algebras

AU - Higson, Nigel

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 1988/1

Y1 - 1988/1

N2 - Let A be a unital C*-algebra and let l denote the Calkin algebra (the bounded operators on a separable Hilbert space, modulo the compact operators K). We prove the following conjecture of M. Karoubi: the algebraic and topological K-theory groups of the tensor product C*-algebra A ⊗ l are equal. The algebra A ⊗ l may be regarded as a "suspension" of the more elementary C*-algebra A ⊗ K; thus Karoubi's conjecture asserts, roughly speaking, that the algebraic and topological K-theories of stable C*-algebras agree.

AB - Let A be a unital C*-algebra and let l denote the Calkin algebra (the bounded operators on a separable Hilbert space, modulo the compact operators K). We prove the following conjecture of M. Karoubi: the algebraic and topological K-theory groups of the tensor product C*-algebra A ⊗ l are equal. The algebra A ⊗ l may be regarded as a "suspension" of the more elementary C*-algebra A ⊗ K; thus Karoubi's conjecture asserts, roughly speaking, that the algebraic and topological K-theories of stable C*-algebras agree.

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U2 - 10.1016/0001-8708(88)90034-5

DO - 10.1016/0001-8708(88)90034-5

M3 - Article

AN - SCOPUS:4344701609

VL - 67

SP - 1

EP - 140

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 1

ER -