On the automorphism group of the generalized conformal structure of a symmetric \(R\)-space
type: Item
instance of: scholarly article
title: On the automorphism group of the generalized conformal structure of a symmetric \(R\)-space
zbMATH Open document ID: 0914.53029
DOI: 10.1016/S0926-2245(97)00015-6
author: Soji Kaneyuki
author: S. G. Gindikin
published in: Differential Geometry and its Applications
publication date: 1999-06-15T00:00:00Z
review text: Let \(g=g_{-1}\oplus g_{0}\oplus g_{1}\) be a simple graded Lie algebra and \(G_{0}\) the group of grade-preserving automorphisms. Then \(G=G_{0}\cdot \text{Inn}(g)\) is an open subgroup of \(\Aut(g)\) and \(U=G_{0}\cdot \exp(g_{1})\) is a subgroup in \(G\). The coset space \(M=G/U\) is called a symmetric \(R\)-space associated with \(g\). These spaces were introduced by \textit{T. Nagano} [Trans. Am. Math. Soc. 118, 428-453 (1965; Zbl 0151.28801)] and \textit{M. Takeuchi} [J. Fac. Sci., Univ. Tokyo, Sect. I 12, 81-191 (1965; Zbl 0144.22804)]. The authors define a generalized conformal structure \(\mathcal K\) on a symmetric \(R\)-space of rank greater than 1. It is a smooth assignment of a cone \(V_{p}\) in each tangent space \(T_{p}M\). A smooth map \(f\) is said to be conformal with respect to \(\mathcal K\) if \(df(V_{p})=V_{f(p)}\) for each \(p\in M\). The group of all \(\mathcal K\)-conformal automorphisms of \(M\) coincides with \(G\).
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 17C20
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 1145932
zbMATH Keywords: generalized conformal structures
zbMATH Keywords: symmetric \(R\)-space
zbMATH Keywords: conformal automorphisms
Wikidata QID: Q115337544
MaRDI profile type: Publication
cites work: On compact generalized Jordan triple systems of the second kind
cites work: Un théorème de Liouville pour les algèbres de Jordan
cites work: Siegel domain realization of pseudo-Hermitian symmetric manifolds
cites work: Q3769563
cites work: Q3788656
cites work: A decomposition theorem for simple Lie groups associated with parahermitian symmetric spaces
cites work: Q4011932
cites work: Pseudo-Hermitian symmetric spaces and Siegel domains over nondegenerate cones
cites work: The Sylvester's law of inertia in simple graded Lie algebras
cites work: Graded Lie algebras and generalized Jordan triple systems
cites work: Q5620817
cites work: Jordan triple systems, 𝑅-spaces, and bounded symmetric domains
cites work: Existence and Conjugacy of Cartan Subalgebras of Jordan Algebras
cites work: Transformation Groups on Compact Symmetric Spaces
cites work: Q3698971
cites work: Q3941676
cites work: Q5520555
cites work: On conjugate loci and cut loci of compact symmetric spaces. II
cites work: Basic transformations of symmetric R-spaces
cites work: On the equivalence problems associated with a certain class of homogeneous spaces
cites work: On the equivalence problems associated with simple graded Lie algebras
cites work: On affine symmetric spaces and the automorphism groups of product manifolds
full work available at URL: s0926-2245(97)00015-6
OpenAlex ID: W1974176780
description: scientific article; zbMATH DE number 1145932