Algebroid prestacks and deformations of ringed spaces

拓扑环式空间上的$\boldsymbol{\tilde{\tau}}$-李代数胚

$\mathcal{L}$-Lie Algebroids over Topological Ringed Spaces

本研究针对拓扑环式空间，引入$\boldsymbol{\tilde{\tau}}$-李代数胚与$\boldsymbol{\tilde{\tau}}$-Gerstenhaber代数，探究标准对应关系在该广义框架中的延伸，丰富了几何与代数结构的统一研究体系。

李代数、量子泊松代数以及李代数连接

Lie algebroids, quantum Poisson algebroids, and Lie algebroid connections

本文研究了覆盖环面的李代数与量子泊松sheaf之间的双射对应关系，并探讨了非平坦李代数连接的构造方法。

Hochschild cohomology for Lie algebroids

We define the Hochschild (co)homology of a ringed space relative to a locally free Lie algebroid. Our definitions mimic those of Swan and Caldararu for an algebraic variety. We show that our (co)homology groups can be computed using suitable standard complexes. Our formulae depend on certain natural structures on jetbundles over Lie algebroids. In an appendix we explain this by showing that such jetbundles are formal groupoids which serve as the formal exponentiation of the Lie algebroid.