Completions of quantum coordinate rings

Abstract

Given an iterated skew polynomial ring C[y 1 ; τ 1 , δ 1 ]...[y n ;τ n ,δ n ] over a complete local ring C with maximal ideal m, we prove, under suitable assumptions, that the completion at the ideal m+(y 1 , y 2 ;.., y n ) is an iterated skew power series ring. Under further conditions, the completion becomes a local, noetherian, Auslander regular domain. Applicable examples include quantum matrices, quantum symplectic spaces, and quantum Euclidean spaces.