Finite Hochschild cohomology without finite global dimension
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finitecohomologydimensiongammaglobalhochschildquestionalgebra
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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.
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