scholarly journals A Galois correspondence for compact group actions on C⁎-algebras

2011 ◽  
Vol 261 (5) ◽  
pp. 1227-1235 ◽  
Author(s):  
Costel Peligrad
Keyword(s):  
Compact Group ◽  
Group Actions ◽  
C Algebras ◽  
Galois Correspondence

scholarly journals An Equivariant Theory for the Bivariant Cuntz Semigroup

2018 ◽  
Vol 61 (2) ◽  
pp. 573-598
Author(s):  
Gabriele N. Tornetta
Keyword(s):  
Compact Group ◽  
Group Actions ◽  
Crossed Products ◽  
C Algebras ◽  
Regularity Properties ◽  
Cuntz Semigroup ◽  
The One ◽  
Equivariant Extension ◽  
Equivariant Theory

AbstractWe provide an equivariant extension of the bivariant Cuntz semigroup introduced in previous work for the case of compact group actions over C*-algebras. Its functoriality properties are explored, and some well-known classification results are retrieved. Connections with crossed products are investigated, and a concrete presentation of equivariant Cuntz homology is provided. The theory that is here developed can be used to define the equivariant Cuntz semigroup. We show that the object thus obtained coincides with the one recently proposed by Gardella [‘Regularity properties and Rokhlin dimension for compact group actions’, Houston J. Math.43(3) (2017), 861–889], and we complement their work by providing an open projection picture of it.

scholarly journals Discrete coactions on C*-algebras

1996 ◽  
Vol 60 (1) ◽  
pp. 118-127 ◽  
Author(s):  
Chi-Keung Ng
Keyword(s):  
Fixed Point ◽  
Compact Group ◽  
Amenable Group ◽  
Group Actions ◽  
Crossed Product ◽  
Discrete Groups ◽  
C Algebras ◽  
Fixed Point Algebra

AbstractWe will consider coactions of discrete groups on C*-algebras and imitate some of the results about compact group actions on C*-algebras. In particular, the crossed product of a reduced coaction ∈ of a discrete amenable group G on A is liminal (respectively, postliminal) if and only if the fixed point algebra of ∈ is. Moreover, we will also consider ergodic coactions on C*-algebras.

scholarly journals Duality for compact group actions on operator algebras and applications: Irreducible inclusions and Galois correspondence

2020 ◽  
Vol 31 (09) ◽  
pp. 2050067
Author(s):  
Costel Peligrad
Keyword(s):  
Fixed Point ◽  
Compact Group ◽  
Operator Algebras ◽  
Group Actions ◽  
Normal Subgroups ◽  
Galois Correspondence ◽  
Duality Property ◽  
Relative Commutant ◽  
Fixed Point Algebra

We consider compact group actions on C*- and W*-algebras. We prove results that relate the duality property of the action (as defined in the Introduction) with other relevant properties of the system such as the relative commutant of the fixed point algebras being trivial (called the irreducibility of the inclusion) and also to the Galois correspondence between invariant C*-subalgebras containing the fixed point algebra and the class of closed normal subgroups of the compact group.

scholarly journals Countable sections for locally compact group actions

1992 ◽  
Vol 12 (2) ◽  
pp. 283-295 ◽  
Author(s):  
Alexander S. Kechris
Keyword(s):  
Compact Group ◽  
Equivalence Relation ◽  
Group Actions ◽  
Locally Compact Group ◽  
Borel Space ◽  
Locally Compact ◽  
Borel Equivalence Relation ◽  
Measurable Section ◽  
Singular Action

AbstractIt has been shown by J. Feldman, P. Hahn and C. C. Moore that every non-singular action of a second countable locally compact group has a countable (in fact so-called lacunary) complete measurable section. This is extended here to the purely Borel theoretic category, consisting of a Borel action of such a group on an analytic Borel space (without any measure). Characterizations of when an arbitrary Borel equivalence relation admits a countable complete Borel section are also established.

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