Noncommutative Knorrer periodicity and noncommutative Kleinian singularities

[摘要] We establish a version of Knorrer's Periodicity Theorem in the context of noncommutative invariant theory. Namely, let A be a left noetherian AS-regular algebra, let f be a normal and regular element of A of positive degree, and take B = A/(f). Then there exists a bijection between the set of isomorphism classes of in decomposable non-free maximal Cohen-Macaulay modules over B and those over (a noncommutative analog of) its second double branched cover (B-#)(#). Our results use and extend the study of twisted matrix factorizations, which was introduced by the first three authors with Cassidy. These results are applied to the noncommutative Kleinian singularities studied by the second and fourth authors with Chan and Zhang. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-15

[关键词] Knorrer periodicity;Maximal Cohen-Macaulay module;Noncommutative invariant theory;Twisted matrix factorization