Results 1  10
of
11
Permanence properties for crossed products and fixed point algebras of finite groups
 Trans. Amer. Math. Soc
"... Abstract. Let α: G → Aut(A) be an action of a finite group G on a C*algebra A. We present some conditions under which properties of A pass to the crossed product C∗(G,A, α) or the fixed point algebra Aα. We mostly consider the ideal property, the projection property, topological dimension zero, and ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Let α: G → Aut(A) be an action of a finite group G on a C*algebra A. We present some conditions under which properties of A pass to the crossed product C∗(G,A, α) or the fixed point algebra Aα. We mostly consider the ideal property, the projection property, topological dimension zero, and pure infiniteness. In many of our results, additional conditions are necessary on the group, the algebra, or the action. Sometimes the action must be strongly pointwise outer, and in a few results it must have the Rokhlin property. When G is finite abelian, we prove that crossed products and fixed point algebras by G preserve topological dimension zero with no condition on the action. We give an example to show that the ideal property and the projection property do not pass to fixed point algebras (even when the group is Z2). The construction also gives an example of a C*algebra B which does not have the ideal property but such that M2(B) does have the ideal property; in fact, M2(B) has the projection property.
Actions of Finite Groups on Substitution Tilings and Their Associated C*algebras
"... The goal of this thesis is to examine the actions of finite symmetry groups on aperiodic tilings. To an aperiodic tiling with finite local complexity arising from a primitive substitution rule one can associate a metric space, transformation groupoids, and C*algebras. Finite symmetry groups of the ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
The goal of this thesis is to examine the actions of finite symmetry groups on aperiodic tilings. To an aperiodic tiling with finite local complexity arising from a primitive substitution rule one can associate a metric space, transformation groupoids, and C*algebras. Finite symmetry groups of the tiling act on each of these objects and we investigate appropriate constructions on each, namely the orbit space, semidirect product groupoids, and crossed product C*algebras respectively. Of particular interest are the crossed product C*algebras; we derive important structure results about them and compute their Ktheory. ii Acknowledgements First and foremost, I would like to thank my wife and the love of my life Anna. This would not have been possible without her love, support, encouragement and friendship. I am also eternally grateful to my wonderful supervisor Thierry Giordano for being generous with excellent advice (both mathematical and otherwise) and financial support throughout my PhD studies. I would also like to thank my family: my mother Susan, my brother Bob, my grandparents Noeline (Nana) and Peter, and my stepfather TJ. In particular I must thank my Nana, who taught me at a young age the importance of continual learning, inquisitiveness, curiosity, and compassion. Mathematically, I would like to thank Ian Putnam, Michael Whittaker, Daniel Gonçalves, David Handelman, and Siegfried Echterhoff for many extremely helpful conversations about this thesis. I would also like to thank NSERC for financial support for the first half of my PhD studies. iii Dedication In memory of my father Ray, who was taken from us before I could finish this degree. We love you, dad. iv
Finite symmetry group actions on substitution tiling C*algebras. arXiv:1207.6301
, 2012
"... For a finite symmetry group G of an aperiodic substitution tiling system (P, ω), we show that the crossed product of the tiling C*algebra Aω by G has real rank zero, tracial rank one, a unique trace, and that order on its Ktheory is determined by the trace. We also show that the action of G on Aω ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
For a finite symmetry group G of an aperiodic substitution tiling system (P, ω), we show that the crossed product of the tiling C*algebra Aω by G has real rank zero, tracial rank one, a unique trace, and that order on its Ktheory is determined by the trace. We also show that the action of G on Aω satisfies the weak Rokhlin property, and that it also satisfies the tracial Rokhlin property provided that Aω has tracial rank zero. In the course of proving the latter we show that Aω is finitely generated. We also provide a link between Aω and the AF algebra Connes associated to the Penrose tilings. 1
GENERALIZED FIXED POINT ALGEBRAS FOR COACTIONS OF LOCALLY COMPACT QUANTUM GROUPS
"... ar ..."
(Show Context)