G-algebras, twistings, and equivalences of graded categories

Abstract

Given Z-graded rings A and B, we study when the categories gr-A and gr-B are equivalent. We relate the Morita-type results of Ahn-Marki and del Rio to the twisting systems introduced by Zhang. Using Z-algebras, we obtain a simple proof of Zhang's main result. This makes the definition of a Zhang twist extremely natural and extends Zhang's results.

13 pages; typos corrected and revised slightly; to appear in Algebras and Representation Theory

References in corpus (1)

• Rings graded equivalent to the Weyl algebra

Cited by in corpus (8)

• Rings graded equivalent to the Weyl algebra
• Compact moduli of noncommutative projective planes
• The noncommutative schemes of generalized Weyl algebras
• The Picard group of the graded module category of a generalized Weyl algebra
• Local duality for connected Z-algebras
• Twisting of graded quantum groups and solutions to the quantum Yang-Baxter equation
• ${\mathbb{Z}}^2$-algebras as noncommutative blow-ups
• A Primer on Twists in the Noncommutative Realm Focusing on Algebra, Representation Theory, and Geometry