On the cohomology of the Weyl algebra, the quantum plane, and the q-Weyl   algebra
  Deformation theory can be used to compute the cohomology of a deformed algebra with coefficients in itself from that of the original. Using the invariance of the Euler-Poincare characteristic under deformation, it is applied here to compute the cohomology of the Weyl algebra, the algebra of the quantum plane, and the q-Weyl algebra. The behavior of the cohomology when q is a root of unity may encode some number theoretic information. 
Murray Gerstenhaber, Anthony Giaquinto
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