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Deformation theory can be used to compute the cohomology of a deformedalgebra with coefficients in itself from that of the original. Using theinvariance of the Euler-Poincare characteristic under deformation, it isapplied here to compute the cohomology of the Weyl algebra, the algebra of thequantum plane, and the q-Weyl algebra. The behavior of the cohomology when q isa root of unity may encode some number theoretic information.

On the cohomology of the Weyl algebra, the quantum plane, and the q-Weyl algebra