C*-ALGEBRAS OF TRIVIAL K-THEORY AND SEMILATTICES

1999 ◽  
Vol 10 (01) ◽  
pp. 93-128 ◽  
Author(s):  
HUAXIN LIN
Keyword(s):  
Direct Limit ◽  
Tensor Products ◽  
Equivalence Classes ◽  
Direct Sums ◽  
C Algebras ◽  
Direct Limits ◽  
One To One ◽  
K Theory ◽  
Essential Extensions ◽  
Distributive Semilattices

We give a class of nuclear C*-algebras which contains [Formula: see text] and is closed under stable isomorphism, ideals, quotients, hereditary subalgebras, tensor products, direct sums, direct limits as well as extensions. We show that this class of C*-algebras is classified by their equivalence classes of projections and there is a one to one correspondence between (unital) C*-algebras in the class and countable distributive semilattices (with largest elements). One of the main results is that essential extensions of a C*-algebras which is a direct limit of finite direct sums of corners of [Formula: see text] by the same type of C*-algebras are still direct limits of finite direct sums of corners of [Formula: see text].

Reduction of Exponential Rank in Direct Limits of C*-Algebras

1994 ◽  
Vol 46 (4) ◽  
pp. 818-853 ◽  
Author(s):  
N. Christopher Phillips
Keyword(s):  
Upper Bound ◽  
Unitary Group ◽  
Direct Limit ◽  
Real Rank ◽  
Direct Sums ◽  
The Real ◽  
Identity Component ◽  
C Algebras ◽  
Direct Limits

AbstractWe prove the following result. Let A be a direct limit of direct sums of C*-algebras of the form C(X) ⊗ Mn, with the spaces X being compact metric. Suppose that there is a finite upper bound on the dimensions of the spaces involved, and suppose that A is simple. Then the C* exponential rank of A is at most 1 + ε, that is, every element of the identity component of the unitary group of A is a limit of exponentials. This is true regardless of whether the real rank of A is 0 or 1.

K-THEORY AND HOMOTOPY OF CERTAIN GROUPS AND INFINITE GRASSMANN SPACES ASSOCIATED WITH C*-ALGEBRAS

1994 ◽  
Vol 05 (03) ◽  
pp. 425-445
Author(s):  
SHUANG ZHANG
Keyword(s):  
Equivalence Classes ◽  
Homotopy Groups ◽  
Grassmann Space ◽  
C Algebras ◽  
K Theory

We determine, in terms of [Formula: see text] and [Formula: see text], the homotopy groups of certain groups of invertibles and of certain equivalence classes in the infinite Grassmann space on a Hilbert C*-[Formula: see text]-module. These results provide various interpretations of [Formula: see text].

Real Af C*-Algebras With K0 of Small Rank

1989 ◽  
Vol 41 (5) ◽  
pp. 786-807
Author(s):  
T. Giordano ◽  
D. E. Handelman
Keyword(s):  
Algebraic Number ◽  
Direct Limit ◽  
Algebraic Number Field ◽  
Morita Equivalence ◽  
Equivalence Classes ◽  
C Algebras ◽  
Finite Dimensional ◽  
Real Algebra ◽  
Rank 2 ◽  
Prime 2

A real AF C*-algebra is the norm closure of a direct limit of finite dimensional real C*-algebras (with real *-algebra maps). When we use the unadorned “AF C*-algebra”, we mean the usual complex version.Let R be a simple AF C*-algebra such that K0(R) is free of rank 2 or 3. The problem is to find (up to Morita equivalence) all real AF C*-algebras A such that AꕕC≅R. This is closely related to the problem of finding all involutions on R [3], [10].For example, when the rank is 2, generically there are 8 such classes. The exceptional cases arise when the ratio of the two generators in K0(R) is a quadratic (algebraic) number, and here there are 4, 5, or 8 Morita equivalence classes, the number depending largely on the behaviour of the prime 2 in the relevant algebraic number field.

scholarly journals Extensions by Simple C*-Algebras: Quasidiagonal Extensions

2005 ◽  
Vol 57 (2) ◽  
pp. 351-399 ◽  
Author(s):  
Huaxin Lin
Keyword(s):  
Equivalence Classes ◽  
Essential Extension ◽  
Unitary Equivalence ◽  
C Algebras ◽  
Continuous Scale ◽  
Image Position ◽  
Essential Extensions ◽  
Universal Coefficient Theorem ◽  
Unital Simple

AbstractLet A be an amenable separable C*-algebra and B be a non-unital but σ-unital simple C*- algebra with continuous scale. We show that two essential extensions τ1 and τ2 of A by B are approximately unitarily equivalent if and only ifIf A is assumed to satisfy the Universal Coefficient Theorem, there is a bijection fromapproximate unitary equivalence classes of the abovementioned extensions to KL(A,M(B)/B). Using KL(A,M(B)/B), we compute exactly when an essential extension is quasidiagonal. We show that quasidiagonal extensions may not be approximately trivial. We also study the approximately trivial extensions.

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 Graded K-theory and K-homology of relative Cuntz–Pimsner algebras and graph C⁎-algebras

2021 ◽  
Vol 496 (2) ◽  
pp. 124822
Author(s):  
Quinn Patterson ◽  
Adam Sierakowski ◽  
Aidan Sims ◽  
Jonathan Taylor
Keyword(s):  
C Algebras ◽  
K Theory

A CATALOGUE OF ORIENTABLE 3-MANIFOLDS TRIANGULATED BY 30 COLORED TETRAHEDRA

2008 ◽  
Vol 17 (05) ◽  
pp. 579-599 ◽  
Author(s):  
MARIA RITA CASALI ◽  
PAOLA CRISTOFORI
Keyword(s):  
Automatic Generation ◽  
Computational Approach ◽  
Equivalence Classes ◽  
Colored Graphs ◽  
One To One ◽  
Genus Two ◽  
Jsj Decompositions

The present paper follows the computational approach to 3-manifold classification via edge-colored graphs, already performed in [1] (with respect to orientable 3-manifolds up to 28 colored tetrahedra), in [2] (with respect to non-orientable 3-manifolds up to 26 colored tetrahedra), in [3] and [4] (with respect to genus two 3-manifolds up to 34 colored tetrahedra): in fact, by automatic generation and analysis of suitable edge-colored graphs, called crystallizations, we obtain a catalogue of all orientable 3-manifolds admitting colored triangulations with 30 tetrahedra. These manifolds are unambiguously identified via JSJ decompositions and fibering structures. It is worth noting that, in the present work, a suitable use of elementary combinatorial moves yields an automatic partition of the elements of the generated crystallization catalogue into equivalence classes, which turn out to be in one-to-one correspondence with the homeomorphism classes of the represented manifolds.

scholarly journals K-theory for certain group C*-algebras

1983 ◽  
Vol 151 (0) ◽  
pp. 209-230 ◽  
Author(s):  
E. Christopher Lance
Keyword(s):  
C Algebras ◽  
K Theory
Sign in / Sign up

Export Citation Format

Share Document