Derived-tame algebras and non-commutative nodal projective curves

导出驯服代数和非交换节点射影曲线

• 批准号: 283334198
• 负责人: Professor Dr. Igor Burban
• 金额: --
• 依托单位: Fachgebiet Computeralgebra und Zahlentheorie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/283334198?language=en
• 关键词: Derived; tame; algebras; non; commutative

The goal of this project is to develop a systematic theory of non-commutative nodal projective curves, similar to the theory of weighted projective lines of Geigle and Lenzing. In particular, we want to clarify when the derived category of coherent sheaves on such a curve admits a tilting object, and describe the classes of tilted algebras arising in this way. We are especially interested in the case when the non-commutative nodal curve we start with (and as a result, the corresponding tilted algebra) has tame derived representation type.Using this approach, we anticipate to treat with new methods old problems about spherical objects and auto-equivalences of the derived category of coherent sheaves on a cycle of projective lines.

该项目的目标是发展非交换节点射影曲线的系统理论，类似于 Geigle 和 Lenzing 的加权射影线理论。特别是，我们想要澄清这种曲线上相干滑轮的派生类别何时允许倾斜物体，并描述以这种方式产生的倾斜代数的类别。我们对我们开始的非交换节点曲线（因此相应的倾斜代数）具有驯服的派生表示类型的情况特别感兴趣。使用这种方法，我们期望用新方法处理有关球形物体的老问题以及射影线循环上相干滑轮的派生类别的自等价性。