论文标题
部分可观测时空混沌系统的无模型预测
A Characteristic free approach to skew-gentle algebras
论文作者
论文摘要
对于每个偏斜的代数，可以根据组合数据分配温和的代数。为了关联两个代数的结构，我们建立了同源性表达和衍生模块类别的回忆。这种方法是没有特征的，尤其是在特征二的特征上也起作用，这对于偏斜代数来说是困难的情况。这样可以解决空旷的问题，并统一地否定和加强已知结果，例如（1）对自我注入性偏斜式代数的完整分类； （2）有资源的维度猜想，澳大利亚和雷坦的猜想，以及凯勒对所有偏斜代数的猜想； （3）偏斜的代数和柔和的代数之间的K理论的精确联系； （4）所有偏斜的代数都是Gorenstein，而偏斜的代数及其柔和的代数共享相同的奇异性类别。
To each skew-gentle algebra, one can assign a gentle algebra in terms of combinatorial data. In order to relate the structures of the two algebras, we establish a homological epimorphism and a recollement of derived module categories. This approach is characteristic free and works in particular also in characteristic two, which is the difficult case for skew-gentle algebras. This allows to solve open problems and to uniformly reprove and strengthen known results, for instance, (1) a complete classification of selfinjective skew-gentle algebras; (2) the finitistic dimension conjecture, Auslander and Reiten's conjecture, and Keller's conjecture hold for all skew-gentle algebras; (3) a precise connection of K-theory between skew-gentle algebras and gentle algebras; (4) all skew-gentle algebras are Gorenstein, and skew-gentle algebras and their gentle algebras share the same singularity categories.
