Twisted tensor product, smooth DG algebras, and noncommutative resolutions of singular curves
Algebraic Geometry
2024-05-09 v1 Category Theory
Rings and Algebras
Abstract
New families of algebras and DG algebras with two simple modules are introduced and described. Using the twisted tensor product operation, we prove that such algebras have finite global dimension, and the resulting DG algebras are smooth. This description allows us to show that some of these DG algebras determine smooth proper noncommutative curves that provide smooth minimal noncommutative resolutions for singular rational curves.
Keywords
Cite
@article{arxiv.2405.04738,
title = {Twisted tensor product, smooth DG algebras, and noncommutative resolutions of singular curves},
author = {Dmitri Orlov},
journal= {arXiv preprint arXiv:2405.04738},
year = {2024}
}
Comments
Dedicated to the blessed memory of Ludwig Dmitrievich Faddeev on the occasion of his 90th birthday, 27 pages