Laura algebras and quasi-directed components

Marcelo Lanzilotta; David Smith

The search session has expired. Please query the service again.

Displaying similar documents to “Laura algebras and quasi-directed components”

Endomorphism rings of regular modules over wild hereditary algebras

Otto Kerner (2003)

Colloquium Mathematicae

Similarity:

Let H be a connected wild hereditary path algebra. We prove that if Z is a quasi-simple regular brick, and [r]Z indecomposable regular of quasi-length r and with quasi-top Z, then $r a d^{r} E n d_{H} ([r] Z) = 0$ .

One-directed indecomposable pure injective modules over string algebras

Mike Prest, Gena Puninski (2004)

Colloquium Mathematicae

Similarity:

We classify one-directed indecomposable pure injective modules over finite-dimensional string algebras.

Relative Auslander-Reiten sequences for quasi-hereditary algebras

Karin Erdmann, José Antonio de la Peña, Corina Sáenz (2002)

Colloquium Mathematicae

Similarity:

Let A be a finite-dimensional algebra which is quasi-hereditary with respect to the poset (Λ, ≤), with standard modules Δ(λ) for λ ∈ Λ. Let ℱ(Δ) be the category of A-modules which have filtrations where the quotients are standard modules. We determine some inductive results on the relative Auslander-Reiten quiver of ℱ(Δ).

On Auslander-Reiten translates in functorially finite subcategories and applications

K. Erdmann, D. Madsen, V. Miemietz (2010)

Colloquium Mathematicae

Similarity:

We consider functorially finite subcategories in module categories over Artin algebras. One main result provides a method, in the setup of bounded derived categories, to compute approximations and the end terms of relative Auslander-Reiten sequences. We also prove an Auslander-Reiten formula for the setting of functorially finite subcategories. Furthermore, we study the category of modules filtered by standard modules for certain quasi-hereditary algebras and we classify precisely when...

Derived tubular algebras and APR-tilts

Hagen Meltzer (2001)

Colloquium Mathematicae

Similarity:

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.

Indecomposable modules in coils

Piotr Malicki, Andrzej Skowroński, Bertha Tomé (2002)

Colloquium Mathematicae

Similarity:

We describe the structure of all indecomposable modules in standard coils of the Auslander-Reiten quivers of finite-dimensional algebras over an algebraically closed field. We prove that the supports of such modules are obtained from algebras with sincere standard stable tubes by adding braids of two linear quivers. As an application we obtain a complete classification of non-directing indecomposable modules over all strongly simply connected algebras of polynomial growth.

Directing components for quasitilted algebras

Flávio Coelho (1999)

Colloquium Mathematicae

Similarity:

We show here that a directing component of the Auslander-Reiten quiver of a quasitilted algebra is either postprojective or preinjective or a connecting component.

Exact Borel subalgebras of quasi-heriditary algebras, I (with an appendix by Leonard Scott).

Steffen König (1995)

Mathematische Zeitschrift

Similarity:

The multiplicity problem for indecomposable decompositions of modules over a finite-dimensional algebra. Algorithms and a computer algebra approach

Piotr Dowbor, Andrzej Mróz (2007)

Colloquium Mathematicae

Similarity:

Given a module M over an algebra Λ and a complete set of pairwise nonisomorphic indecomposable Λ-modules, the problem of determining the vector $m (M) = {(m_{X})}_{X \in} \in ℕ^{}$ such that $M ≅ ⨁_{X \in} X^{m_{X}}$ is studied. A general method of finding the vectors m(M) is presented (Corollary 2.1, Theorem 2.2 and Corollary 2.3). It is discussed and applied in practice for two classes of algebras: string algebras of finite representation type and hereditary algebras of type $̃_{p, q}$ . In the second case detailed algorithms are given (Algorithms 4.5...

Selfinjective algebras of strictly canonical type

Marta Kwiecień, Andrzej Skowroński (2009)

Colloquium Mathematicae

Similarity:

We develop the representation theory of selfinjective algebras of strictly canonical type and prove that their Auslander-Reiten quivers admit quasi-tubes maximally saturated by simple and projective modules.

Integral schur algebras for GL2.

Jie Du (1992)

Manuscripta mathematica

Similarity:

On split-by-nilpotent extensions

Ibrahim Assem, Dan Zacharia (2003)

Colloquium Mathematicae

Similarity:

Let A and R be two artin algebras such that R is a split extension of A by a nilpotent ideal. We prove that if R is quasi-tilted, or tame and tilted, then so is A. Moreover, generalizations of these properties, such as laura and shod, are also inherited. We also study the relationship between the tilting R-modules and the tilting A-modules.

Indecomposable Modules over Multicoil Algebras.

A. Skowronski, I. Assem (1992)

Mathematica Scandinavica

Similarity:

Koszul duality for N-Koszul algebras

Roberto Martínez-Villa, Manuel Saorín (2005)

Colloquium Mathematicae

Similarity:

The correspondence between the category of modules over a graded algebra and the category of graded modules over its Yoneda algebra was studied in [8] by means of $A_{\infty}$ algebras; this relation is very well understood for Koszul algebras (see for example [5],[6]). It is of interest to look for cases such that there exists a duality generalizing the Koszul situation. In this paper we will study N-Koszul algebras [1], [7], [9] for which such a duality exists.

Cycle-finite algebras with almost all indecomposable modules of projective or injective dimension at most one

Adam Skowyrski (2013)

Colloquium Mathematicae

Similarity:

We describe the structure of artin algebras for which all cycles of indecomposable modules are finite and almost all indecomposable modules have projective or injective dimension at most one.

On the structure of indecomposable modules over Artin algebras

Andrzej Skowroński (1984)

Colloquium Mathematicae

Similarity:

The composite of irreducible morphisms in regular components

Claudia Chaio, María Inés Platzeck, Sonia Trepode (2011)

Colloquium Mathematicae

Similarity:

We study when the composite of n irreducible morphisms between modules in a regular component of the Auslander-Reiten quiver is non-zero and lies in the n+1-th power of the radical ℜ of the module category. We prove that in this case such a composite belongs to $ℜ^{\infty}$ . We apply these results to characterize those string algebras having n irreducible morphisms between band modules such that their composite is a non-zero morphism in $ℜ^{n + 1}$ .

Koszul and quasi-Koszul algebras obtained by tilting

R. M. Aquino, E. L. Green, E. N. Marcos (2002)

Colloquium Mathematicae

Similarity:

Given a finite-dimensional algebra, we present sufficient conditions on the projective presentation of the algebra modulo its radical for a tilted algebra to be a Koszul algebra and for the endomorphism ring of a tilting module to be a quasi-Koszul algebra. One condition we impose is that the algebra has global dimension no greater than 2. One of the main techniques is studying maps between the direct summands of the tilting module. Some applications are given. We also show that a Brenner-Butler...

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...

The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences.

Claus Michael Ringel (1991)

Mathematische Zeitschrift

Similarity:

Quasi *-algebras of measurable operators

Fabio Bagarello, Camillo Trapani, Salvatore Triolo (2006)

Studia Mathematica

Similarity:

Non-commutative $L^{p}$ -spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p ≥ 2 they are also proved to possess a sufficient family of bounded positive sesquilinear forms with certain invariance properties. CQ*-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (,₀) with a sufficient family of bounded positive tracial sesquilinear forms can be represented...

Wild Hereditary Artin Algebras and Linear Methods.

Dagmar Baer (1986)

Manuscripta mathematica

Similarity:

A note on quasitilted algebras

Andrzej Skowroński, Adam Skowyrski (2014)

Colloquium Mathematicae

Similarity:

We provide a characterization of artin algebras without chains of nonzero homomorphisms between indecomposable finitely generated modules starting with an injective module and ending with a projective module.

On the existence of super-decomposable pure-injective modules over strongly simply connected algebras of non-polynomial growth

Stanisław Kasjan, Grzegorz Pastuszak (2014)

Colloquium Mathematicae

Similarity:

Assume that k is a field of characteristic different from 2. We show that if Γ is a strongly simply connected k-algebra of non-polynomial growth, then there exists a special family of pointed Γ-modules, called an independent pair of dense chains of pointed modules. Then it follows by a result of Ziegler that Γ admits a super-decomposable pure-injective module if k is a countable field.

On the number of terms in the middle of almost split sequences over cycle-finite artin algebras

Piotr Malicki, José Peña, Andrzej Skowroński (2014)

Open Mathematics

Similarity:

We prove that the number of terms in the middle of an almost split sequence in the module category of a cycle-finite artin algebra is bounded by 5.

Iterated tilted and tilted stably hereditary algebras

Jessica Lévesque (2003)

Colloquium Mathematicae

Similarity:

We prove that a stably hereditary bound quiver algebra A = KQ/I is iterated tilted if and only if (Q,I) satisfies the clock condition, and that in this case it is of type~Q. Furthermore, A is tilted if and only if (Q,I) does not contain any double-zero.

Tilting theory - an introduction

I. Assem (1990)

Banach Center Publications

Similarity:

Locally convex quasi C*-algebras and noncommutative integration

Camillo Trapani, Salvatore Triolo (2015)

Studia Mathematica

Similarity:

We continue the analysis undertaken in a series of previous papers on structures arising as completions of C*-algebras under topologies coarser that their norm topology and we focus our attention on the so-called locally convex quasi C*-algebras. We show, in particular, that any strongly *-semisimple locally convex quasi C*-algebra (𝔛,𝔄₀) can be represented in a class of noncommutative local L²-spaces.