Displaying similar documents to “On the classification of simple inductive limit C * -algebras. I: The reduction theorem.”

Extensions of certain real rank zero C * -algebras

Marius Dadarlat, Terry A. Loring (1994)

Annales de l'institut Fourier

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G. Elliott extended the classification theory of A F -algebras to certain real rank zero inductive limits of subhomogeneous C * -algebras with one dimensional spectrum. We show that this class of C * -algebras is not closed under extensions. The relevant obstruction is related to the torsion subgroup of the K 1 -group. Perturbation and lifting results are provided for certain subhomogeneous C * -algebras.

Notes on a class of simple C*-algebras with real rank zero.

Kenneth R. Goodearl (1992)

Publicacions Matemàtiques

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A construction method is presented for a class of simple C*-algebras whose basic properties -including their real ranks- can be computed relatively easily, using linear algebra. A numerival invariant attached to the construction determines wether a given algebra has real rank 0 or 1. Moreover, these algebras all have stable rank 1, and each nonzero hereditary sub-C*-algebra contains a nonzero projection, yet there are examples in which the linear span of the projections is not dense....

Isosceles sets.

Ionin, Yury J. (2009)

The Electronic Journal of Combinatorics [electronic only]

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Spaces with fibered approximation property in dimension n

Taras Banakh, Vesko Valov (2010)

Open Mathematics

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A metric space M is said to have the fibered approximation property in dimension n (briefly, M ∈ FAP(n)) if for any ɛ > 0, m ≥ 0 and any map g: 𝕀 m × 𝕀 n → M there exists a map g′: 𝕀 m × 𝕀 n → M such that g′ is ɛ-homotopic to g and dim g′ (z × 𝕀 n) ≤ n for all z ∈ 𝕀 m. The class of spaces having the FAP(n)-property is investigated in this paper. The main theorems are applied to obtain generalizations of some results due to Uspenskij [11] and Tuncali-Valov [10].

Mutating seeds: types 𝔸 and 𝔸 ˜ .

Ibrahim Assem, Christophe Reutenauer (2012)

Annales mathématiques Blaise Pascal

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In the cases 𝔸 and 𝔸 ˜ , we describe the seeds obtained by sequences of mutations from an initial seed. In the 𝔸 ˜ case, we deduce a linear representation of the group of mutations which contains as matrix entries all cluster variables obtained after an arbitrary sequence of mutations (this sequence is an element of the group). Nontransjective variables correspond to certain subgroups of finite index. A noncommutative rational series is constructed, which contains all this information. ...