论文标题
Koszul扭曲的Calabi-yau代数上的扭曲的双链结构
Twisted bi-symplectic structure on Koszul twisted Calabi-Yau algebras
论文作者
论文摘要
对于Koszul Artin-Schelter常规代数（也称为Twisted calabi-yau代数），我们表明它具有“扭曲”的双链结构，可以将其视为由Pantev，to to to to to to to to to n oet n，vaquieé和Vezzosi引入的转移符号结构的非交换性和扭曲的类似物。这种结构在分区复合物和代数的扭曲的旋转复合物之间产生了准同态，并且可以看作是范登·伯格（Van den Bergh）非共同庞加莱二元性的DG增强。它还在其衍生表示方案上诱导了扭曲的符合结构。
For a Koszul Artin-Schelter regular algebra (also called twisted Calabi-Yau algebra), we show that it has a "twisted" bi-symplectic structure, which may be viewed as a noncommutative and twisted analogue of the shifted symplectic structure introduced by Pantev, Toën, Vaquié and Vezzosi. This structure gives a quasi-isomorphism between the tangent complex and the twisted cotangent complex of the algebra, and may be viewed as a DG enhancement of Van den Bergh's noncommutative Poincaré duality; it also induces a twisted symplectic structure on its derived representation schemes.
