Noncommutative Knorrer Periodicity and Noncommutative Kleinian Singularities

SMC Author

Andrew Conner

SMC Affiliated Work

1

Status

Faculty

School

School of Science

Department

Math/Computer Science

Document Type

Article

Publication Date

12-15-2019

Publication / Conference / Sponsorship

Journal of Algebra

Description/Abstract

We establish a version of Knörrer'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)" role="presentation">. Then there exists a bijection between the set of isomorphism classes of indecomposable non-free maximal Cohen-Macaulay modules over B and those over (a noncommutative analog of) its second double branched cover (B#)#" role="presentation">. 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.

DOI

10.1016/j.jalgebra.2019.09.001.

ISSN

0021-8693

Volume

540

First Page

234

Last Page

273

Disciplines

Mathematics

Rights

Open access

Original Citation

Conner, Andrew; Kirkman, Ellen; Moore, W. Frank; and Walton, Chelsea. Noncommutative Knorrer Periodicity and Noncommutative Kleinian Singularities. Journal of Algebra 540 (2019) pp. 234-273. doi: 10.1016/j.jalgebra.2019.09.001

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