Group actions, orbit spaces, and noncommutative deformation theory; pp. 364–369Full article in PDF format | doi: 10.3176/proc.2010.4.16
Consider the action of a group G on an ordinary commutative k-variety X = Spec(A). In this note we define the category of A–G-modules and their deformation theory. We then prove that this deformation theory is equivalent to the deformation theory of modules over the noncommutative k-algebra A[G] = A#G. The classification of orbits can then be studied over a commutative ring, and we give an example of this on surface cyclic singularities.
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