Noncommutative Knorrer Periodicity and Noncommutative Kleinian Singularities
SMC Affiliated Work
School of Science
Publication / Conference / Sponsorship
Journal of Algebra
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.
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
Conner, Andrew; Kirkman, Ellen; Frank, Moore W.; and Walton, Chelsea. Noncommutative Knorrer Periodicity and Noncommutative Kleinian Singularities (2019). Journal of Algebra. 540, 234-273. 10.1016/j.jalgebra.2019.09.001. [article]. https://digitalcommons.stmarys-ca.edu/school-science-faculty-works/1123