2016
DOI: 10.7900/jot.2014dec22.2061
|View full text |Cite
|
Sign up to set email alerts
|

Independent resolutions for totally disconnected dynamical systems. II. $C^*$-algebraic case

Abstract: We develop the notion of independent resolutions for crossed products attached to totally disconnected dynamical systems. If such a crossed product admits an independent resolution of finite length, then its K-theory can be computed (at least in principle) by analysing the corresponding six-term exact sequences. Building on our previous paper on algebraic independent resolutions, we give a criterion for the existence of finite length independent resolutions. Moreover, we illustrate our ideas in various concret… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

1
8
0

Year Published

2016
2016
2021
2021

Publication Types

Select...
4
2
1

Relationship

0
7

Authors

Journals

citations
Cited by 13 publications
(9 citation statements)
references
References 10 publications
1
8
0
Order By: Relevance
“…This leads to the conjecture that A(S) is isomorphic to p∈P O p for all families P, see [BOS16, Conjecture 6.5]. e) By b), A(S) embeds canonically into Q p (S) and this embedding yields an isomorphism in K-theory, at least for |P| ≤ 2, see [LN16,BOS16].…”
Section: A First Look At the K-theorymentioning
confidence: 98%
See 1 more Smart Citation
“…This leads to the conjecture that A(S) is isomorphic to p∈P O p for all families P, see [BOS16, Conjecture 6.5]. e) By b), A(S) embeds canonically into Q p (S) and this embedding yields an isomorphism in K-theory, at least for |P| ≤ 2, see [LN16,BOS16].…”
Section: A First Look At the K-theorymentioning
confidence: 98%
“…S = N ⋊ P , where P is the free abelian submonoid of N × generated by a family P of relatively prime numbers. For such semigroups, nontrivial partial results emerged in the recent past [LN16,BOS16]. These results lead to intriguing questions and relate to conjectures about C * -algebras of k-graphs, see [BOS16, Conjecture 5.11].…”
Section: A First Look At the K-theorymentioning
confidence: 99%
“…where r j ∈ 2O K is any element in the unique nontrivial class of the quotient ring 2O K /2ω j O for each j = 0, 1, 2. Because 2O K = 2ω j O (r j + 2ω j O) for each j ∈ {0, 1, 2}, another application of [31,Lemma 6.3] shows that if F ⊂ J(O O × ) is a finite collection of constructible right ideals such that 2O K × 2O × K = S∈F S, then F contains {2ω j O × 2ω j O × , (r j + 2ω j O) × 2ω j O × } for j = {0, 1, 2}. An analogue of this fact also holds with an arbritary constructible ideal (r + 2xO K ) × 2xO × K ∈ J(O O × ) in place of 2O K × 2O × K and {2xω j O × 2xω j O × , (r + xr j + 2xω j O) × 2xω j O × } in place of {2ω j O × 2ω j O × , (r j + 2ω j O) × 2ω j O × } for j = 0, 1, 2.…”
Section: O ∩ Okmentioning
confidence: 99%
“…The importance of the globalization problem lies in the possibility to relate partial actions with global ones and this way try to move from global results to the partial setting, producing more general facts, as well as to obtain applications to the global case in situations in which partial actions appear naturally, as it occurred in [23]. Thus facts about globalization from [4] were used in [237] with respect to K -theory of reduced C * -algebras of 0-F-inverse semigroups, in [225] in the K -theoretic study of reduced crossed products attached to totally disconnected dynamical systems, and in [26] for partial flows with application to Lyapunov functions. In addition, globalizable partial actions were essential for the development of Galois Theory of partial group actions in [123], for the elaboration of the concept of a partial Hopf (co)action in [72], as well as in a series of ring theoretic and Galois theoretic investigations in [27,29,30,32,35,39,41,49,50,69,77,98,99,101,104,106,171,176,252,253].…”
Section: Mathematics Subject Classificationmentioning
confidence: 99%