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arXiv · 1208.0346

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

Murray Gerstenhaber·Anthony Giaquinto
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Abstract

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.

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Murray Gerstenhaber, Anthony Giaquinto. 2012-08-01. On the cohomology of the Weyl algebra, the quantum plane, and the q-Weyl algebra. https://arxiv.org/abs/1208.0346

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