Completions of quantum coordinate rings
Abstract
Given an iterated skew polynomial ring C[y1;t1,d1]ldots [yn;tn,dn] over a complete local ring C with maximal ideal m, we prove, under suitable assumptions, that the completion at the ideal m + < y1,y2,ldots,yn> is an iterated skew power series ring. Under further conditions, this completion is a local, noetherian, Auslander regular domain. Applicable examples include quantum matrices, quantum symplectic spaces, and quantum Euclidean space.
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