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COMPLETIONS OF QUANTUM COORDINATE RINGS

By Linhong Wang

Abstract

Abstract. Given an iterated skew polynomial ring C[y1; τ1, δ1]...[yn; τn, δn] over a complete local ring C with maximal ideal m, we prove, under suitable assumptions, that the completion at the ideal m+〈y1, y2,..., yn 〉 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. 1

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