Isomorphism and Morita equivalence classes for crossed products of irrational rotation algebras by cyclic subgroups of SL2(Z)

2018 ◽  
Vol 275 (11) ◽  
pp. 3208-3243
Author(s):  
Christian Bönicke ◽  
Sayan Chakraborty ◽  
Zhuofeng He ◽  
Hung-Chang Liao
Keyword(s):  
Morita Equivalence ◽  
Equivalence Classes ◽  
Irrational Rotation ◽  
Crossed Products ◽  
Cyclic Subgroups

Strong Morita Equivalence for Heisenberg C*-Algebras and the Positive Cones of Their K 0-Groups

1988 ◽  
Vol 40 (04) ◽  
pp. 833-864 ◽  
Author(s):  
Judith A. Packer
Keyword(s):  
Heisenberg Group ◽  
Morita Equivalence ◽  
Equivalence Classes ◽  
Crossed Products ◽  
C Algebras ◽  
Projective Representations ◽  
Discrete Heisenberg Group ◽  
Strong Morita Equivalence

In [14] we began a study of C*-algebras corresponding to projective representations of the discrete Heisenberg group, and classified these C*-algebras up to *-isomorphism. In this sequel to [14] we continue the study of these so-called Heisenberg C*-algebras, first concentrating our study on the strong Morita equivalence classes of these C*-algebras. We recall from [14] that a Heisenberg C*-algebra is said to be of class i, i ∊ {1, 2, 3}, if the range of any normalized trace on its K 0 group has rank i as a subgroup of R; results of Curto, Muhly, and Williams [7] on strong Morita equivalence for crossed products along with the methods of [21] and [14] enable us to construct certain strong Morita equivalence bimodules for Heisenberg C*-algebras.

scholarly journals EPSILON-STRONGLY GROUPOID-GRADED RINGS, THE PICARD INVERSE CATEGORY AND COHOMOLOGY

2019 ◽  
Vol 62 (1) ◽  
pp. 233-259 ◽  
Author(s):  
PATRIK NYSTEDT ◽  
JOHAN ÖINERT ◽  
HÉCTOR PINEDO
Keyword(s):  
Cohomology Group ◽  
Equivalence Classes ◽  
Crossed Products ◽  
Graded Rings ◽  
Classical Construction

AbstractWe introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call, generalized epsilon-crossed products and show that these coincide with the class of epsilon-strongly groupoid-graded rings. We then use generalized epsilon-crossed groupoid products to obtain a generalization, from the group-graded situation to the groupoid-graded case, of the bijection from a certain second cohomology group, defined by the grading and the functor from the groupoid in question to the Picard inverse category, to the collection of equivalence classes of rings epsilon-strongly graded by the groupoid.

scholarly journals HILBERT C*-BIMODULES OF FINITE INDEX AND APPROXIMATION PROPERTIES OF C*-ALGEBRAS

2017 ◽  
Vol 60 (2) ◽  
pp. 321-331
Author(s):  
MARZIEH FOROUGH ◽  
MASSOUD AMINI
Keyword(s):  
Finite Index ◽  
Morita Equivalence ◽  
Discrete Groups ◽  
Crossed Products ◽  
Approximation Properties ◽  
C Algebras ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
The Stability

AbstractLet A and B be arbitrary C*-algebras, we prove that the existence of a Hilbert A–B-bimodule of finite index ensures that the WEP, QWEP, and LLP along with other finite-dimensional approximation properties such as CBAP and (S)OAP are shared by A and B. For this, we first study the stability of the WEP, QWEP, and LLP under Morita equivalence of C*-algebras. We present examples of Hilbert A–B-bimodules, which are not of finite index, while such properties are shared between A and B. To this end, we study twisted crossed products by amenable discrete groups.

scholarly journals Classification of pointed fusion categories of dimension p3 up to weak Morita Equivalence

2020 ◽  
pp. 2140008
Author(s):  
Kevin Maya ◽  
Adriana Mejía Castaño ◽  
Bernardo Uribe
Keyword(s):  
Complete Classification ◽  
Global Dimension ◽  
Morita Equivalence ◽  
Equivalence Classes ◽  
Fusion Categories ◽  
Dimension Formula ◽  
Equivalent Categories

We give a complete classification of pointed fusion categories over [Formula: see text] of global dimension [Formula: see text] for [Formula: see text] any odd prime. We proceed to classify the equivalence classes of pointed fusion categories of dimension [Formula: see text] and we determine which of these equivalence classes have equivalent categories of modules.

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