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Displaying similar documents to “Cohomology Groups of Infinite Dimensional Algebras.”

Distinguishing derived equivalence classes using the second Hochschild cohomology group

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.

Special biserial algebras with no outer derivations

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...

Hochschild cohomology of generalized multicoil algebras

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.