Hochschild cohomology of Auslander algebras
Dieter Happel (1990)
Banach Center Publications
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Dieter Happel (1990)
Banach Center Publications
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Generalov, A.I. (2004)
Zapiski Nauchnykh Seminarov POMI
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Rolf Farnsteiner (1988)
Mathematische Zeitschrift
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Generalov, A.I. (2002)
Zapiski Nauchnykh Seminarov POMI
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Piotr Malicki, Andrzej Skowroński (2014)
Colloquium Mathematicae
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We determine the Hochschild cohomology of all finite-dimensional generalized multicoil algebras over an algebraically closed field, which are the algebras for which the Auslander-Reiten quiver admits a separating family of almost cyclic coherent components. In particular, the analytically rigid generalized multicoil algebras are described.
Deena Al-Kadi (2010)
Colloquium Mathematicae
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We study the second Hochschild cohomology group of the preprojective algebra of type D₄ over an algebraically closed field K of characteristic 2. We also calculate the second Hochschild cohomology group of a non-standard algebra which arises as a socle deformation of this preprojective algebra and so show that the two algebras are not derived equivalent. This answers a question raised by Holm and Skowroński.
Rolf Farnsteiner (1991)
Mathematische Zeitschrift
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E. Marcos, R. Martínez-Villa, Ma. Martins (2004)
Open Mathematics
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Let A be a k-algebra and G be a group acting on A. We show that G also acts on the Hochschild cohomology algebra HH ⊙ (A) and that there is a monomorphism of rings HH ⊙ (A) G→HH ⊙ (A[G]). That allows us to show the existence of a monomorphism from HH ⊙ (Ã) G into HH ⊙ (A), where à is a Galois covering with group G.
Jens P. Nielsen (1980)
Mathematica Scandinavica
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Shurygin, Vadim V., Smolyakova, Larisa B. (2001)
Lobachevskii Journal of Mathematics
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Holm, Thorsten (2000)
Beiträge zur Algebra und Geometrie
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Jaume Aguadé (1981)
Mathematische Zeitschrift
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K. Peters, J.F. Carlson, D.K. Nakano (1995)
Mathematische Annalen
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Hagen Meltzer (2001)
Colloquium Mathematicae
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Petter Andreas Bergh (2006)
Colloquium Mathematicae
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Let M be a finitely generated module over an Artin algebra. By considering the lengths of the modules in the minimal projective resolution of M, we obtain the Betti sequence of M. This sequence must be bounded if M is eventually periodic, but the converse fails to hold in general. We give conditions under which it holds, using techniques from Hochschild cohomology. We also provide a result which under certain conditions guarantees the existence of periodic modules. Finally, we study...
Adam Skowyrski (2013)
Colloquium Mathematicae
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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.
Nicole Snashall, Rachel Taillefer (2010)
Colloquium Mathematicae
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We consider the socle deformations arising from formal deformations of a class of Koszul self-injective special biserial algebras which occur in the study of the Drinfeld double of the generalized Taft algebras. We show, for these deformations, that the Hochschild cohomology ring modulo nilpotence is a finitely generated commutative algebra of Krull dimension 2.
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.
Andrzej Skowroński, Adam Skowyrski (2014)
Colloquium Mathematicae
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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.
Helmut Strade, Jörg Feldvoss (1992)
Manuscripta mathematica
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