Dorfmeister, Josef Proof of the radical conjecture of homogeneous Kähler manifolds. (English) Zbl 0681.53030 Nagoya Math. J. 114, 77-122 (1989). The paper contains a proof of the so-called radical conjecture formulated by the author in 1986 [CMS Conf. Proc. 5, 189-208 (1986; Zbl 0589.53064)]. It claims that for any Kähler algebra (\({\mathfrak g},{\mathfrak k},j,\rho)\) such that \({\mathfrak g}={\mathfrak r}+j{\mathfrak r}+{\mathfrak k}\), where \({\mathfrak r}\) is a solvable ideal of \({\mathfrak g}\), we have \({\mathfrak g}={\mathfrak s}+{\mathfrak k}\), where \({\mathfrak s}\cap {\mathfrak k}=0\), j\({\mathfrak s}\subset {\mathfrak s}\) (after an inessential change of j) and \({\mathfrak s}\) is a solvable Kähler algebra. The results have been already used for the proof of the Gindikin-Vinberg conjecture about the structure of homogeneous Kähler manifolds given by the author and Nakajima. Reviewer: A.L.Onishchik Cited in 2 Documents MSC: 53C30 Differential geometry of homogeneous manifolds 32M10 Homogeneous complex manifolds 53C55 Global differential geometry of Hermitian and Kählerian manifolds Keywords:radical conjecture; Kähler algebra; Gindikin-Vinberg conjecture; homogeneous Kähler manifolds Citations:Zbl 0589.53064 PDFBibTeX XMLCite \textit{J. Dorfmeister}, Nagoya Math. J. 114, 77--122 (1989; Zbl 0681.53030) Full Text: DOI