Displaying similar documents to “Unital extensions of A F -algebras by purely infinite simple algebras”

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.

On the trivial extensions of tubular algebras

Jerzy Białkowski (2004)

Colloquium Mathematicae

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The aim of this note is to give an affirmative answer to a problem raised in [9] by J. Nehring and A. Skowroński, concerning the number of nonstable ℙ₁(K)-families of quasi-tubes in the Auslander-Reiten quivers of the trivial extensions of tubular algebras over algebraically closed fields K.

On minimal non-tilted algebras

Flávio U. Coelho, José A. de la Peña, Sonia Trepode (2008)

Colloquium Mathematicae

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A minimal non-tilted triangular algebra such that any proper semiconvex subcategory is tilted is called a tilt-semicritical algebra. We study the tilt-semicritical algebras which are quasitilted or one-point extensions of tilted algebras of tame hereditary type. We establish inductive procedures to decide whether or not a given strongly simply connected algebra is tilted.

The vanishing of self-extensions over n-symmetric algebras of quasitilted type

Maciej Karpicz, Marju Purin (2014)

Colloquium Mathematicae

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A ring Λ satisfies the Generalized Auslander-Reiten Condition ( ) if for each Λ-module M with E x t i ( M , M ⊕ Λ ) = 0 for all i > n the projective dimension of M is at most n. We prove that this condition is satisfied by all n-symmetric algebras of quasitilted type.

A double commutant theorem for purely large C*-subalgebras of real rank zero corona algebras

P. W. Ng (2009)

Studia Mathematica

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Let 𝓐 be a unital separable simple nuclear C*-algebra such that ℳ (𝓐 ⊗ 𝓚) has real rank zero. Suppose that ℂ is a separable simple liftable and purely large unital C*-subalgebra of ℳ (𝓐 ⊗ 𝓚)/ (𝓐 ⊗ 𝓚). Then the relative double commutant of ℂ in ℳ (𝓐 ⊗ 𝓚)/(𝓐 ⊗ 𝓚) is equal to ℂ.

Grzegorczyk Algebras Revisited

Michał M. Stronkowski (2018)

Bulletin of the Section of Logic

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We provide simple algebraic proofs of two important facts, due to Zakharyaschev and Esakia, about Grzegorczyk algebras.

Schwartz kernel theorem in algebras of generalized functions

Vincent Valmorin (2010)

Banach Center Publications

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A new approach to the generalization of Schwartz’s kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of G ∞ -generalized functions class are given. A straightforward relationship between the classical and the generalized...

Homomorphisms of commutative Banach algebras and extensions to multiplier algebras with applications to Fourier algebras

E. Kaniuth, A. T. Lau, A. Ülger (2007)

Studia Mathematica

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Let A and B be semisimple commutative Banach algebras with bounded approximate identities. We investigate the problem of extending a homomorphism φ: A → B to a homomorphism of the multiplier algebras M(A) and M(B) of A and B, respectively. Various sufficient conditions in terms of B (or B and φ) are given that allow the construction of such extensions. We exhibit a number of classes of Banach algebras to which these criteria apply. In addition, we prove a polar decomposition for homomorphisms...

Some remarks on Q -algebras

Nicolas Th. Varopoulos (1972)

Annales de l'institut Fourier

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We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that ℓ p , ( 1 ≤ p ≤ ∞ ) are Q algebras and that A n = ℨ L 1 ( Z ; 1 + | n | α ) is a Q -algebra if and only if α > 1 / 2 .