Hochschild上同调、高阶结构与operad理论

本项目主要利用operad理论研究结合代数的Hochschild上同调与同调的高阶结构与有关的同调猜想。我们将利用弱自同伦技术与代数Morse理论计算一些重要代数的Hochschild上同调群与同调群及其高阶结构；研究Hochschild（上）同调复形的B无穷结构在Koszul对偶与扭Poincaré对偶下的性态；我们将系统地发展Tate-Hochschild上同调理论；利用形变量子化与半经典极限研究与Hochschild上同调理论有关的一些同调猜想。

This projet studies, via operad theory, higher structures over Hochschild (co)homology of associative algebras and related homological conjectures. We will compute Hochschild (co)homology groups and higher structures over them for some important algebras via the technique of weak self-homotopies and algebraic Morse theory; we will investigate the behavior of B-infinity structure over Hochschild (co)chain complexes under Koszul duality and skew Poincaré duality; we will study several homological conjectures concerning Hochschild theory via deformation quantization and semi-classical limits.