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Proof of the radical conjecture of homogeneous Kähler manifolds. (English) Zbl 0681.53030

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

MSC:

53C30 Differential geometry of homogeneous manifolds
32M10 Homogeneous complex manifolds
53C55 Global differential geometry of Hermitian and Kählerian manifolds

Citations:

Zbl 0589.53064
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