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-Poincaré 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. © 2013.
Gerstenhaber, M., & Giaquinto, A. (2014). On the cohomology of the Weyl algebra, the quantum plane, and the q-Weyl algebra. Journal of Pure and Applied Algebra, 218(5), 879–887. https://doi.org/10.1016/j.jpaa.2013.10.006