Twisted Tensor Product, Smooth DG Algebras, and Noncommutative Resolutions of Singular Curves

被引：0
|
作者：
Orlov, Dmitri [1 ]
机构：
[1] Russian Acad Sci, Steklov Math Inst, Moscow, Russia
来源：
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS | 2024年 / 58卷 / 04期
关键词：
noncommutative algebraic geometry; derived noncommutative schemes; differential graded algebras; perfect modules and complexes; 2 SIMPLE MODULES; TRIANGULATED CATEGORIES; DIMENSIONS; SCHEMES;
D O I：
10.1134/S001626632404004X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 that 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.
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页码：384 / 408
页数：25
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