An Introduction to K-Theory for C*-Algebras

Rørdam, Mikael; Larsen, F.; Laustsen, Niels Jakob

doi:10.1017/cbo9780511623806

Cited by 346 publications

(399 citation statements)

References 0 publications

Supporting

Mentioning

357

Contrasting

Unclassified

Order By: Relevance

“…Since K 0 (C(X)) ∼ = K 0 (X) as Abelian groups for any compact Hausdorff space X (consult [22]), the proof of our theorem is thus complete.…”

Section: Lemma 3 ([6])mentioning

confidence: 81%

See 1 more Smart Citation

Toeplitz Algebras on Strongly Pseudoconvex Domains

Cao¹

2007

Nagoya Mathematical Journal

View full text Add to dashboard Cite

Abstract. In the present paper, it is proved that the K0-group of a Toeplitz algebra on any strongly pseudoconvex domain is always isomorphic to the K0-group of the relative continuous function algebra, and is thus isomorphic to the topological K 0 -group of the boundary of the relative domain. Further there exists a ring isomorphism between the K0-groups of Toeplitz algebras and the Chern classes of the relative boundaries of strongly pseudoconvex domains. As applications of our main result, K-groups of Toeplitz algebras on some special strongly pseudoconvex domains are computed. Our results show that the Toeplitz algebras on strongly pseudoconvex domains have rich structures, which deeply depend on the topological structures of relative domains. In addition, the first cohomology groups of Toeplitz algebras are also computed.

show abstract

“…Since K 0 (C(X)) ∼ = K 0 (X) as Abelian groups for any compact Hausdorff space X (consult [22]), the proof of our theorem is thus complete.…”

Section: Lemma 3 ([6])mentioning

confidence: 81%

“…Thus we obtain a ring isomorphism between K 0 (J ∂Ω ) ⊗ Q and H ev (∂Ω; Q) by Theorem 1 and by using the Chern character (see [22]). …”

Section: Lemma 3 ([6])mentioning

confidence: 93%

Toeplitz Algebras on Strongly Pseudoconvex Domains

Cao¹

2007

Nagoya Mathematical Journal

View full text Add to dashboard Cite

show abstract

“…With this operation, V(R) is a commutative monoid, and it is conical, meaning that a + b = 0 in V(R) only when a = b = 0. Whenever A is a C*-algebra, the monoid V(A) agrees with the monoid of equivalence classes of projections in M ∞ (A) with respect to the equivalence relation given by e ∼ f if and only if there is a partial isometry w in M ∞ (A) such that e = ww * and f = w * w; see [6, 4.6.2 and 4.6.4] or [17,Exercise 3.11].…”

Section: Preliminary Definitionsmentioning

confidence: 99%

K-theory for the tame C⁎-algebra of a separated graph

Ara

Exel

2015

Journal of Functional Analysis

View full text Add to dashboard Cite

show abstract

“…In this Section, we briefly recall the definition of the K-theory for C * -algebras, the noncommutative analogue of the topological K-theory, and also the definition of the K-homology groups (see, for instance, [19,42,98,108,160,183] for further information).…”

Section: Noncommutative Topologymentioning

confidence: 99%