A construction of actions on Kirchberg algebras which induce given actions on their K-groups

By Takeshi Katsura. 2006

55 citations recorded by the source corpus.

Abstract We prove that every action of a finite group all of whose Sylow subgroups are cyclic on the K-theory of a Kirchberg algebra can be lifted to an action on the Kirchberg algebra. The proof uses a construction of Kirchberg algebras generalizing the one of Cuntz-Krieger algebras, and a result on modules over finite groups. As a corollary, every automorphism of the K-theory of a Kirchberg algebra can be lifted to an automorphism of the Kirchberg algebra with same order.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/37c9d38df0e6d8c49e235e01f1ddae6135826777

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In Algebra and Number Theory

1. Aidan Sims
2. Enrique Pardo
3. L. O. Clark
4. Charles Starling
5. R. Exel
6. Ben Steinberg
7. P. Ara
8. Mark V. Lawson

In Geometry and Topology

1. Enrique Pardo
2. R. Exel
3. Aidan Sims
4. Charles Starling
5. L. O. Clark
6. Ben Steinberg
7. Mikhailo Dokuchaev

In Mathematical Physics

1. Enrique Pardo
2. Aidan Sims
3. R. Exel
4. L. O. Clark
5. Charles Starling
6. Ben Steinberg
7. Mark V. Lawson
8. P. Ara

Citations in the corpus

• Self-similar graphs, a unified treatment of Katsura and Nekrashevych C*-algebras (2014, methodology): “In possession of the graph, the action of Z, and the cocycle ϕ constructed above, we apply our construction and we find that OG,E is isomorphic to Katsura’s OA,B .”
• Simplicity of algebras associated to non-Hausdorff groupoids (2018, background): “In [18], Katsura associates a C∗-algebra to a pair of square integer matrices A,B and studies their properties.”
• The tight groupoid of an inverse semigroup (2014, methodology): “To mention an example of interest to us, in [6] and [7] a unified treatment was given to a certain class of C*-algebras studied by Katsura in [9], alongside Nekrashevych’s C*algebras introduced and discussed in [12], [13] and [14].”
• A class of C*-algebras generalizing both graph algebras and homeomorphism C*-algebras IV, pure infiniteness (2008, unknown): “In [ Ka8 ], we will extend his result using our construction.”