FINITE HOCHSCHILD COHOMOLOGY WITHOUT FINITE GLOBAL DIMENSION

By R. Buchweitz, Edward L. Green, D. Madsen, Ø. Solberg. 2004

128 citations recorded by the source corpus.

Dieter Happel asked the following question: If the $n$-th Hochschild cohomology group of a finite dimensional algebra $\Gamma$ over a field vanishes for all sufficiently large $n$, is the global dimension of $\Gamma$ finite? We give a negative answer to this question.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5d45226318bb4a4df533d3cd27cb2e72e4e26b2c

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In Algebra and Number Theory

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In Mathematical Physics

Citations in the corpus

MULTIPLICATIVE STRUCTURES FOR KOSZUL ALGEBRAS (2005, background): “be found in [2], where, for algebras in this class, HH(Λ) is a finitely generated algebra.”
Derived Categories (2016, background): “(If the base field K is perfect, one can show that A is homologically smooth over it; see [60] and [35].”
The hochschild cohomology ring of a class of special biserial algebras (2008, methodology): “In the case N = 1, the Hochschild cohomology ring of the algebra Λ1 with m = 1 is discussed in [1], where q-analogues of Λ1 were used to answer negatively a question of Happel, in that they have finite dimensional Hochschild cohomology ring but are of infinite global Date: March 11, 2008.”
Hochschild (Co)Homology Dimension (2004, methodology): “Recall the minimal projective resolution constructed in [5].”
The Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra (2014, unknown): “A counter-example was exhibited in [8].”