Complex structures on the complexification of a real Lie algebra

Complex Manifolds

Yamada Takumi¹ 

[1] Department of Mathematics, Shimane University, Nishikawatsu-cho 1060,Matsue, Japan;

关键词: nilmanifold;    dolbeault cohomology group;    complex structure;    53c30;    57t15;    22e25;   

DOI  :  10.1515/coma-2018-0010

来源: DOAJ

【 摘 要 】

Let g = a+b be a Lie algebra with a direct sum decomposition such that a and b are Lie subalgebras. Then, we can construct an integrable complex structure J̃ on h = ℝ(gℂ) from the decomposition, where ℝ(gℂ) is a real Lie algebra obtained from gℂby the scalar restriction. Conversely, let J̃ be an integrable complex structure on h = ℝ(gℂ). Then, we have a direct sum decomposition g = a + b such that a and b are Lie subalgebras. We also investigate relations between the decomposition g = a + b and dim Hs.t∂̄J̃ (hℂ).

【 授权许可】

Unknown