Cohomology of algebras of dihedral type. I.
Generalov, A.I. (2002)
Zapiski Nauchnykh Seminarov POMI
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Generalov, A.I. (2002)
Zapiski Nauchnykh Seminarov POMI
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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.
Dieter Happel (1990)
Banach Center Publications
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Rolf Farnsteiner (1991)
Mathematische Zeitschrift
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Jens P. Nielsen (1980)
Mathematica Scandinavica
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Jaume Aguadé (1981)
Mathematische Zeitschrift
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Yemon Choi (2010)
Banach Center Publications
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We revisit the old result that biflat Banach algebras have the same cyclic cohomology as C, and obtain a quantitative variant (which is needed in separate, joint work of the author on the simplicial and cyclic cohomology of band semigroup algebras). Our approach does not rely on the Connes-Tsygan exact sequence, but is motivated strongly by its construction as found in [2] and [5].
Helmut Strade, Jörg Feldvoss (1992)
Manuscripta mathematica
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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.
Rolf Farnsteiner (1988)
Mathematische Zeitschrift
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Douglas C. Ravenel (1976/77)
Mathematische Zeitschrift
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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...
König, Steffen, Xi, Changchang (1999)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Generalov, A.I., Kachalova, M.A. (2005)
Zapiski Nauchnykh Seminarov POMI
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Arunas Liulevicius (1968)
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.