Cassidy, Thomas; Conner, Andrew; Kirkman, Ellen; Moore, W. Frank Periodic free resolutions from twisted matrix factorizations. (English) Zbl 1378.16003 J. Algebra 455, 137-163 (2016). Summary: The notion of a matrix factorization was introduced by Eisenbud in the commutative case in his study of bounded (periodic) free resolutions over complete intersections. Since then, matrix factorizations have appeared in a number of applications. In this work, we extend the notion of (homogeneous) matrix factorizations to regular normal elements of connected graded algebras over a field. Next, we relate the category of twisted matrix factorizations to an element over a ring and certain Zhang twists. We also show that in the setting of a quotient of a ring of finite global dimension by a normal regular element, every sufficiently high syzygy module is the cokernel of some twisted matrix factorization. Furthermore, we show that in the noetherian AS-regular setting, there is an equivalence of categories between the homotopy category of twisted matrix factorizations and the singularity category of the hypersurface, following work of D. Orlov [Prog. Math. 270, 503–531 (2009; Zbl 1200.18007)]. Cited in 5 Documents MSC: 16E05 Syzygies, resolutions, complexes in associative algebras 16E35 Derived categories and associative algebras 16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) Keywords:matrix factorization; Zhang twist; singularity category; minimal free resolution; maximal Cohen-Macaulay Citations:Zbl 1200.18007 Software:BERGMAN; Macaulay2 × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Anick, David J., Noncommutative graded algebras and their Hilbert series, J. 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