BIMSA > Seminar on Algebraic, Complex Geometry and Singularities Geometric structure of nilpotent Lie algebras and cohomological aspects of Yau Algebras.
Geometric structure of nilpotent Lie algebras and cohomological aspects of Yau Algebras.
组织者
丘成栋
演讲者
刘志文
时间
2024年11月29日 21:00 至 22:00
地点
Online
摘要
From complex analytic hypersurfaces with isolated singularities (or higher-codimensional singularities), we obtain important algebraic structures known as Yau algebras, which are finite-dimensional complex nilpotent Lie algebras. A natural question arises: which types of finite-dimensional complex nilpotent Lie algebras can be realized as Yau algebras? If this is the case, we can regard these Lie algebras as "geometric." In this talk, I will explore how tools from the theory of complex geometry of manifolds can be employed to analyze several cohomological aspects of Lie algebras (including De Rham,Dolbeault, Bott-Chern, and Aeppli cohomologies) and examine whether certain special Hermitian metrics exist on these Lie algebras.