Operations on Hochschild Chains and Cochains

Hochschild 链和 Cochains 上的操作

• 批准号: 0070717
• 负责人: Dmitry Tamarkin
• 金额: $ 9.09万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2003-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070717&HistoricalAwards=false
• 关键词: Operations; Hochschild; Chains; Cochains

The investigator and his colleagues are going to study operations on deformation complexes of various algebraic structures: in particular, operations on Hochschild cochains and chains of an associative algebra, and the deformation complex of d-algebras. The knowledge of operations on Hochschild (co) chains should be useful for Index theory on a (degenerate) Poisson manifold, which is of great importance for Poisson geometry. Also, the investigator is trying to find a general simple construction of an operad acting on a deformation complex of a general algebraic structure. This can be helpful in studying deformations of such objects as Hopf algebras.

研究者和他的同事将研究各种代数结构的变形复合体的运算：特别是Hochschild协链和关联代数的链的运算，以及d-代数的变形复合体。关于Hochschild （co）链运算的知识对于（退化）泊松流形上的指标理论是有用的，这在泊松几何中是非常重要的。此外，研究者还试图找到一个作用于一般代数结构的变形复合体的算子的一般简单构造。这对研究Hopf代数等对象的变形是有帮助的。