Displaying similar documents to “Stability of C * -algebras is not a stable property.”

Generalized canonical algebras and standard stable tubes

Andrzej Skowroński (2001)

Colloquium Mathematicae

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We introduce a new wide class of finite-dimensional algebras which admit families of standard stable tubes (in the sense of Ringel [17]). In particular, we prove that there are many algebras of arbitrary nonzero (finite or infinite) global dimension whose Auslander-Reiten quivers admit faithful standard stable tubes.

Prolongations and stability in dynamical systems

J. Auslander, P. Seibert (1964)

Annales de l'institut Fourier

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Les auteurs étudient la notion de prolongement au sens de T. Ura et ses relations avec la notion d’ensembles positivement invariants. La stabilité au sens de Liapounoff est équivalente à l’invariance par prolongement. Les auteurs dégagent ensuite la notion de “prolongements abstraits” et les notions de stabilité correspondantes; la stabilité absolue (associée au prolongement minimal transitif) et la stabilité asymptotique jouent un rôle important.

Selfinjective algebras of tubular type

Jerzy Białkowski, Andrzej Skowroński (2002)

Colloquium Mathematicae

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We classify all tame self/injective algebras having simply connected Galois coverings and the stable Auslander-Reiten quivers consisting of stable tubes. Moreover, the classification of nondomestic polynomial growth standard self/injective algebras is completed.

Stable elements of Banach and Fréchet algebras

Graham Allan (1998)

Studia Mathematica

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We introduce an algebraic notion-stability-for an element of a commutative ring. It is shown that the stable elements of Banach algebras, and of Fréchet algebras, may be simply described. Part of the theory of power-series embeddings, given in [1] and [4], is seen to be of a purely algebraic nature. This approach leads to other natural questions.

Symmetric special biserial algebras of euclidean type

Rafał Bocian, Andrzej Skowroński (2003)

Colloquium Mathematicae

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We classify (up to Morita equivalence) all symmetric special biserial algebras of Euclidean type, by algebras arising from Brauer graphs.

Left-right projective bimodules and stable equivalences of Morita type

Zygmunt Pogorzały (2001)

Colloquium Mathematicae

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We study a connection between left-right projective bimodules and stable equivalences of Morita type for finite-dimensional associative algebras over a field. Some properties of the category of all finite-dimensional left-right projective bimodules for self-injective algebras are also given.