The Cohomology Ring of a Monomial Algebra.
E.L. Green, D. Zacharia (1994)
Manuscripta mathematica
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E.L. Green, D. Zacharia (1994)
Manuscripta mathematica
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Generalov, A.I. (2004)
Zapiski Nauchnykh Seminarov POMI
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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.
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.
Helmut Strade, Rolf Farnsteiner (1991)
Mathematische Zeitschrift
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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.
Jaume Aguadé (1981)
Mathematische Zeitschrift
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Generalov, A.I., Kachalova, M.A. (2005)
Zapiski Nauchnykh Seminarov POMI
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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.
Pearson, Kelly Jeanne (2001)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Dieter Happel (1990)
Banach Center Publications
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Ibrahim Assem, Juan Carlos Bustamante, Patrick Le Meur (2011)
Colloquium Mathematicae
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Let A be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of A with coefficients in the bimodule A vanishes if and only if A is representation-finite and simply connected (in the sense of Bongartz and Gabriel), if and only if the Euler characteristic of Q equals the number of indecomposable non-uniserial projective-injective A-modules (up to isomorphism). Moreover, if this is the case, then all the higher Hochschild cohomology...
Akira Masuoka (2003)
Banach Center Publications
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Douglas C. Ravenel (1976/77)
Mathematische Zeitschrift
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Generalov, A.I. (2002)
Zapiski Nauchnykh Seminarov POMI
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Jens P. Nielsen (1980)
Mathematica Scandinavica
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