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.
Generalov, A.I. (2002)
Zapiski Nauchnykh Seminarov POMI
Similarity:
Alicja Jaworska-Pastuszak, Andrzej Skowroński (2013)
Colloquium Mathematicae
Similarity:
We describe the structure of finite-dimensional algebras of domestic representation type over an algebraically closed field whose Auslander-Reiten quiver consists of generalized standard and semiregular components. Moreover, we prove that this class of algebras contains all special biserial algebras whose Auslander-Reiten quiver consists of semiregular components.
Zygmunt Pogorzały, Mirosława Sufranek (2004)
Colloquium Mathematicae
Similarity:
The class of n-fundamental algebras is introduced. It is a subclass of string algebras. For n-fundamental algebras we study the problem of when the Auslander-Reiten quiver contains, at the beginning or at the end, a component which is not generalized standard.
Andrzej Skowroński, Kunio Yamagata (2003)
Colloquium Mathematicae
Similarity:
We describe the structure of all selfinjective artin algebras having at least three nonperiodic generalized standard Auslander-Reiten components. In particular, all selfinjective artin algebras having a generalized standard Auslander-Reiten component of Euclidean type are described.
Ibrahim Assem (2009)
Colloquium Mathematicae
Similarity:
We define a notion of left section in an Auslander-Reiten component, by weakening one of the axioms for sections. We derive a generalisation of the Liu-Skowroński criterion for tilted algebras, then apply our results to describe the Auslander-Reiten components lying in the left part of an artin algebra.
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...
Andrzej Skowroński, Kunio Yamagata (2015)
Colloquium Mathematicae
Similarity:
We provide a characterization of all finite-dimensional selfinjective algebras over a field K which are socle equivalent to a prominent class of selfinjective algebras of tilted type.
Rafał Bocian, Andrzej Skowroński (2003)
Colloquium Mathematicae
Similarity:
We classify (up to Morita equivalence) all symmetric special biserial algebras of Euclidean type, by algebras arising from Brauer graphs.
Hagen Meltzer (2001)
Colloquium Mathematicae
Similarity:
Giorgia Bellomonte, Camillo Trapani (2013)
Studia Mathematica
Similarity:
Flávio U. Coelho, José A. de la Peña, Sonia Trepode (2008)
Colloquium Mathematicae
Similarity:
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.
Marta Kwiecień, Andrzej Skowroński (2009)
Colloquium Mathematicae
Similarity:
In continuation of our article in Colloq. Math. 116.1, we give a complete description of the symmetric algebras of strictly canonical type by quivers and relations, using Brauer quivers.
Chia Zargeh (2021)
Communications in Mathematics
Similarity:
In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.
Grzegorz Bobiński, Andrzej Skowroński (2001)
Colloquium Mathematicae
Similarity:
We give a complete description of finite-dimensional selfinjective algebras of Euclidean tilted type over an algebraically closed field whose all nonperiodic Auslander-Reiten components are almost regular. In particular, we describe the tame selfinjective finite-dimensional algebras whose all nonperiodic Auslander-Reiten components are almost regular and generalized standard.
J. Słomiński
Similarity:
CONTENTSIntroduction.................................................................................................................... 5§ 1. Fundamental concepts for quasi-algebras..................................................... 5§ 2. Peano-algebras.................................................................................................... 13§ 3. Peano-algebras and free quasi-algebras....................................................... 25§ 4. Theorems concerning free...
Flávio U. Coelho, Ma. I. R. Martins, Bertha Tomé (2004)
Colloquium Mathematicae
Similarity:
We study the simple connectedness and strong simple connectedness of the following classes of algebras: (tame) coil enlargements of tame concealed algebras and n-iterated coil enlargement algebras.
J. Słomiński
Similarity:
CONTENTSINTRODUCTION...................................................................................................................................................................... 31. TERMS NOTATION AND LEMMAS.................................................................................................................................. 4A. Quasi-algebras and 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.
Daniel W. Stroock (1976)
Colloquium Mathematicae
Similarity:
Arzumanyan, V.A. (2005)
Zapiski Nauchnykh Seminarov POMI
Similarity:
Cedilnik, A. (2000)
Acta Mathematica Universitatis Comenianae. New Series
Similarity:
G. Grätzer, J. Sichler (1974)
Colloquium Mathematicae
Similarity:
Marcus Tressl (2002)
Banach Center Publications
Similarity:
Kazimierz Urbanik (1969)
Colloquium Mathematicum
Similarity:
Noriaki Kamiya, Daniel Mondoc, Susumu Okubo (2011)
Banach Center Publications
Similarity:
In this paper we give a review on δ-structurable algebras. A connection between Malcev algebras and a generalization of δ-structurable algebras is also given.
Ewa Graczyńska, Andrzej Wroński (1978)
Colloquium Mathematicum
Similarity:
Camillo Trapani (2005)
Banach Center Publications
Similarity:
The main facts about unbounded C*-seminorms on partial *-algebras are reviewed and the link with the representation theory is discussed. In particular, starting from the more familiar case of *-algebras, we examine C*-seminorms that are defined from suitable families of positive linear or sesquilinear forms, mimicking the construction of the Gelfand seminorm for Banach *-algebras. The admissibility of these forms in terms of the (unbounded) C*-seminorms they generate is characterized. ...