Finite Hochschild cohomology without finite global dimension
  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. 
R.-O. Buchweitz, E. L. Green, D. Madsen, O. Solberg