Finite Hochschild Cohomology without Finite Global Dimension

  title={Finite Hochschild Cohomology without Finite Global Dimension},
  author={Edward L. Green and Dag \Oivind Madsen and \OYVIND and Solberg}
In [9], Dieter Happel asked the following question: If the Hochschild cohomology groups HH(Γ) of a finite dimensional algebra Γ over a field k vanish for all sufficiently large n, is the global dimension of Γ finite? We give a negative answer to this question. Indeed, consider the finite dimensional algebras Λ = Λq = k〈x, y〉/(x , xy + qyx, y) for some field k and q in k. These algebras, intensely studied already by Rainer Schulz [13] to exhibit other pathologies, are all four dimensional, of… CONTINUE READING
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