Bimodule resolution of the Liu-Schulz algebras.
Kosovskaya, N.Yu. (2005)
Zapiski Nauchnykh Seminarov POMI
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Kosovskaya, N.Yu. (2005)
Zapiski Nauchnykh Seminarov POMI
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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.
T. Müldner (1975)
Colloquium Mathematicae
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Terry A. Loring (1993)
Mathematica Scandinavica
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Warren Dicks (1988)
Publicacions Matemàtiques
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A direct proof of Braun's characterization of Azumaya algebras is given.
Markus Linckelmann (1996)
Mathematische Zeitschrift
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Marta Kwiecień, Andrzej Skowroński (2005)
Colloquium Mathematicae
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We give necessary and sufficient conditions for a wing of an Auslander-Reiten quiver of a selfinjective algebra to be the wing of the radical of an indecomposable projective module. Moreover, a characterization of indecomposable Nakayama algebras of Loewy length ≥ 3 is obtained.
Rørdam, Mikael (1997)
Documenta Mathematica
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Fidel Hernández Advíncula, Eduardo do Nascimento Marcos (2007)
Colloquium Mathematicae
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The aim of this work is to characterize the algebras which are standardly stratified with respect to any order of the simple modules. We show that such algebras are exactly the algebras with all idempotent ideals projective. We also deduce as a corollary a characterization of hereditary algebras, originally due to Dlab and Ringel.
Antipov, M.A. (2005)
Zapiski Nauchnykh Seminarov POMI
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M. Barot, O. Mendoza (2006)
Colloquium Mathematicae
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An easy explicit construction is given for a full and faithful functor from the bounded derived category of modules over an associative algebra A to the stable category of the repetitive algebra of A. This construction simplifies the one given by Happel.
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.
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.
R. Sridharan, R. Parimala, M.A. Knus (1981/82)
Inventiones mathematicae
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Jerzy Białkowski, Andrzej Skowroński (2007)
Colloquium Mathematicae
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We describe the stable module categories of the self-injective finite-dimensional algebras of finite representation type over an algebraically closed field which are Calabi-Yau (in the sense of Kontsevich).
Reiten, Idun (1998)
Documenta Mathematica
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Helmut Lenzing, Andrzej Skowroński (2003)
Colloquium Mathematicae
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We develop the representation theory of selfinjective algebras which admit Galois coverings by the repetitive algebras of algebras whose derived category of bounded complexes of finite-dimensional modules is equivalent to the derived category of coherent sheaves on a weighted projective line with virtual genus greater than one.
Marta Kwiecień, Andrzej Skowroński (2009)
Colloquium Mathematicae
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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.
Alicja Jaworska (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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We investigate the categorical behaviour of morphisms between indecomposable projective modules over a special biserial algebra A over an algebraically closed field, which are associated to arrows of the Gabriel quiver of A.
Goldberg, Moshe (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Røordam, Mikael (2001)
Documenta Mathematica
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Michael Barot, Dirk Kussin, Helmut Lenzing (2013)
Colloquium Mathematicae
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Canonical algebras, introduced by C. M. Ringel in 1984, play an important role in the representation theory of finite-dimensional algebras. They also feature in many other mathematical areas like function theory, 3-manifolds, singularity theory, commutative algebra, algebraic geometry and mathematical physics. We show that canonical algebras are characterized by a number of interesting extremal properties (among concealed-canonical algebras, that is, the endomorphism rings of tilting...