Covariant representations for possibly singular actions on $C^*$-algebras

2020 ◽  
Vol 549 ◽  
pp. 1-94
Author(s):  
Daniel Beltiţă ◽  
Hendrik Grundling ◽  
Karl-Hermann Neeb
Keyword(s):  
C Algebras ◽  
Covariant Representations

scholarly journals Crossed products of C*-algebras by *-endomorphisms

1993 ◽  
Vol 54 (2) ◽  
pp. 204-212 ◽  
Author(s):  
P. J. Stacey
Keyword(s):  
Universal Property ◽  
Crossed Products ◽  
C Algebras ◽  
Covariant Representations

AbstractCrossed products of C*-algebras by *-endomorphisms are defined in terms of a universal property for covariant representations implemented by families of isometries and some elementary properties of covariant representations and crossed products are obtained.

scholarly journals A higher category approach to twisted actions on c* -algebras

2012 ◽  
Vol 56 (2) ◽  
pp. 387-426 ◽  
Author(s):  
Alcides Buss ◽  
Ralf Meyer ◽  
Chenchang Zhu
Keyword(s):  
Classical Group ◽  
Group Actions ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Equivariant Maps ◽  
C Algebras ◽  
Covariant Representations ◽  
Group Case ◽  
Morita Equivalent

AbstractC*-algebras form a 2-category with *-homomorphisms or correspondences as morphisms and unitary intertwiners as 2-morphisms. We use this structure to define weak actions of 2-categories, weakly equivariant maps between weak actions and modifications between weakly equivariant maps. In the group case, we identify the resulting notions with known ones, including Busby–Smith twisted actions and the equivalence of such actions, covariant representations and saturated Fell bundles. For 2-groups, weak actions combine twists in the sense of Green, and Busby and Smith.The Packer–Raeburn Stabilization Trick implies that all Busby–Smith twisted group actions of locally compact groups are Morita equivalent to classical group actions. We generalize this to actions of strict 2-groupoids.

COMPACTLY-ALIGNED DISCRETE PRODUCT SYSTEMS, AND GENERALIZATIONS OF ${\mathcal O}_\infty$

1999 ◽  
Vol 10 (06) ◽  
pp. 721-738 ◽  
Author(s):  
NEAL J. FOWLER
Keyword(s):  
Lattice Structure ◽  
Positive Cone ◽  
Algebraic Characterization ◽  
Product System ◽  
C Algebras ◽  
Covariant Representations ◽  
Product Systems ◽  
System P ◽  
Discrete Semigroups

The universal C*-algebras of discrete product systems generalize the Toeplitz–Cuntz algebras and the Toeplitz algebras of discrete semigroups. We consider a semigroup P which is quasi-lattice ordered in the sense of Nica, and, for a product system p : E→ P, we study those representations of E, called covariant, which respect the lattice structure of P. We identify a class of product systems, which we call compactly aligned, for which there is a purely C*-algebraic characterization of covariance, and study the algebra [Formula: see text] which is universal for covariant representations of E. Our main theorem is a characterization of the faithful representations of [Formula: see text] when P is the positive cone of a free product of totally-ordered amenable groups.

An Introduction to K-Theory for C*-Algebras

2000 ◽  
Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  
C Algebras ◽  
K Theory

scholarly journals Optimal transport and unitary orbits in C⁎-algebras

2021 ◽  
Vol 281 (5) ◽  
pp. 109068
Author(s):  
Bhishan Jacelon ◽  
Karen R. Strung ◽  
Alessandro Vignati
Keyword(s):  
Optimal Transport ◽  
C Algebras

Non‐associative C *‐algebras

2021 ◽  
pp. 111-153
Author(s):  
Ángel Rodríguez Palacios ◽  
Miguel Cabrera García
Keyword(s):  
C Algebras
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