Non-invariant deformations of left-invariant complex structures on compact Lie groups

2020/04/06 by Hiroaki Ishida, Hisashi Kasuya, Ishida, Hiroaki +1
Mathematics · Physics and Astronomy · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2004.02523

openalex publication_date 2020/04/06 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We consider deformations of left-invariant complex structures on simply connected semisimple compact Lie groups which are a priori non-invariant. Computing their cohomologies, we show that they are not actually biholomorphic to left-invariant (right-invariant) complex structures.

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