Displaying similar documents to “Varieties of modules over tubular algebras”

CB-degenerations and rigid degenerations of algebras

Adam Hajduk (2006)

Colloquium Mathematicae

Similarity:

The main aim of this note is to prove that if k is an algebraically closed field and a k-algebra A₀ is a CB-degeneration of a finite-dimensional k-algebra A₁, then there exists a factor algebra Ā₀ of A₀ of the same dimension as A₁ such that Ā₀ is a CB-degeneration of A₁. As a consequence, Ā₀ is a rigid degeneration of A₁, provided A₀ is basic.

Characterizing Non-Matrix Properties of Varieties of Algebras in the Language of Forbidden Objects

Finogenova, Olga (2012)

Serdica Mathematical Journal

Similarity:

2010 Mathematics Subject Classification: 16R10, 16R40. We discuss characterizations of some non-matrix properties of varieties of associative algebras in the language of forbidden objects. Properties under consideration include the Engel property, Lie nilpotency, permutativity. We formulate a few open problems. * The author acknowledges support from the Russian Foundation for Basic Research, grant 10-01-00524.

On a separation of orbits in the module variety for domestic canonical algebras

Piotr Dowbor, Andrzej Mróz (2008)

Colloquium Mathematicae

Similarity:

Given a pair M,M' of finite-dimensional modules over a domestic canonical algebra Λ, we give a fully verifiable criterion, in terms of a finite set of simple linear algebra invariants, deciding if M and M' lie in the same orbit in the module variety, or equivalently, if M and M' are isomorphic.

On the problem of axiomatization of tame representation type

Stanisław Kasjan (2002)

Fundamenta Mathematicae

Similarity:

Associative algebras of fixed dimension over algebraically closed fields of fixed characteristic are considered. It is proved that the class of algebras of tame representation type is axiomatizable. Moreover, finite axiomatizability of this class is equivalent to the conjecture that the algebras of tame representation type form a Zariski-open subset in the variety of algebras.

Tilting slice modules over minimal 2-fundamental algebras

Zygmunt Pogorzały, Karolina Szmyt (2008)

Colloquium Mathematicae

Similarity:

A class of finite-dimensional algebras whose Auslander-Reiten quivers have starting but not generalized standard components is investigated. For these components the slices whose slice modules are tilting are considered. Moreover, the endomorphism algebras of tilting slice modules are characterized.

Hyperidentities in many-sorted algebras

Klaus Denecke, Somsak Lekkoksung (2009)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

The theory of hyperidentities generalizes the equational theory of universal algebras and is applicable in several fields of science, especially in computers sciences (see e.g. [2,1]). The main tool to study hyperidentities is the concept of a hypersubstitution. Hypersubstitutions of many-sorted algebras were studied in [3]. On the basis of hypersubstitutions one defines a pair of closure operators which turns out to be a conjugate pair. The theory of conjugate pairs of additive closure...

On two tame algebras with super-decomposable pure-injective modules

Stanisław Kasjan, Grzegorz Pastuszak (2011)

Colloquium Mathematicae

Similarity:

Let k be a field of characteristic different from 2. We consider two important tame non-polynomial growth algebras: the incidence k-algebra of the garland 𝒢₃ of length 3 and the incidence k-algebra of the enlargement of the Nazarova-Zavadskij poset 𝒩 𝓩 by a greatest element. We show that if Λ is one of these algebras, then there exists a special family of pointed Λ-modules, called an independent pair of dense chains of pointed modules. Hence, by a result of Ziegler, Λ admits a super-decomposable...