• Corpus ID: 117764570

# Twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs

@article{Whitehead2013TwistedRC,
title={Twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs},
journal={arXiv: Operator Algebras},
year={2013}
}
To each finitely aligned higher-rank graph $\Lambda$ and each $\mathbb{T}$-valued 2-cocycle on $\Lambda$, we associate a family of twisted relative Cuntz-Krieger algebras. We show that each of these algebras carries a gauge action, and prove a gauge-invariant uniqueness theorem. We describe an isomorphism between the fixed point algebras for the gauge actions on the twisted and untwisted relative Cuntz-Krieger algebras. We show that the quotient of a twisted relative Cuntz-Krieger algebra by a…
7 Citations
• Mathematics
• 2014
Given a system of coverings of k-graphs, we show that the second cohomology of the resulting (k + 1)-graph is isomorphic to that of any one of the k-graphs in the system, and compute the semifinite
• Mathematics
Integral Equations and Operator Theory
• 2015
Given a system of coverings of k-graphs, we show that the second cohomology of the resulting (k + 1)-graph is isomorphic to that of any one of the k-graphs in the system, and compute the semifinite
• Mathematics
• 2017
We develop methods for computing graded K-theory of C*-algebras as defined in terms of Kasparov theory. We establish graded versions of Pimsner's six-term sequences for graded Hilbert bimodules whose
• Mathematics
• 2015
We construct a noncommutative deformation of odd-dimensional spheres that preserves the natural partition of the $(2N+1)$-dimensional sphere into $(N+1)$-many solid tori. This generalizes the case
• Mathematics
Journal of Noncommutative Geometry
• 2018
We find multipullback quantum odd-dimensional spheres equipped with natural $U(1)$-actions that yield the multipullback quantum complex projective spaces constructed from Toeplitz cubes as
• Mathematics
Documenta Mathematica
• 2014
We introduce twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs and give a comprehensive treatment of their fundamental structural properties. We establish

## References

SHOWING 1-10 OF 37 REFERENCES

• Mathematics
Proceedings of the Edinburgh Mathematical Society
• 2003
Abstract We consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz–Krieger algebras. We describe a variant of the Cuntz–Krieger relations which applies to
• A. Sims
• Mathematics
• 2006
Abstract We produce a complete description of the lattice of gauge-invariant ideals in ${{C}^{*}}(\Lambda )$ for a finitely aligned $k$ -graph $\Lambda$ . We provide a condition on $\Lambda$ under
• Mathematics
Ergodic Theory and Dynamical Systems
• 1997
We construct a universal Cuntz–Krieger algebra ${\cal {AO}}_A$, which is isomorphic to the usual Cuntz–Krieger algebra ${\cal O}_A$ when $A$ satisfies condition $(I)$ of Cuntz and Krieger. The Cuntz
• Mathematics
• 1997
We associate to each locally finite directed graphGtwo locally compact groupoidsGandG(★). The unit space ofGis the space of one–sided infinite paths inG, andG(★) is the reduction ofGto the space of
• Mathematics
• 2001
We classify the gauge-invariant ideals in the C*-algebras of infinite directed graphs, and describe the quotients as graph algebras. We then use these results to identify the gauge-invariant
• Mathematics
• 1980
In this paper we present a class of C*-algebras and point out its close relationship to topological Markov chains, whose theory is part of symbolic dynamics. The C*-algebra construction starts from a
Given a row-finite k-graph Λ with no sources we investigate the K-theory of the higher rank graph C *-algebra, C * (Λ). When k = 2 we are able to give explicit formulae to calculate the K-groups of C
• Mathematics
• 2004
We use a Heegaard splitting of the topological 3-sphere as a guiding principle to construct a family of its noncommutative deformations. The main technical point is an identification of the universal