Classification of semisimple Levi-Tanaka algebras
type: Item
instance of: scholarly article
title: Classification of semisimple Levi-Tanaka algebras
zbMATH Open document ID: 0999.17039
DOI: 10.1007/BF01759376
author: Costantino Medori
author: Mauro Nacinovich
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2001-02-04T00:00:00Z
review text: A partial complex structure on a graded real Lie algebra \(g= \bigoplus_{p\in \mathbb{Z}} g_p\) is an \(\mathbb{R}\)-linear map \(J:g_{-1}\to g_{-1}\) such that \(J^2=- \text{Id}_{g_{-1}}\) and \([JX,JY]= [X,Y]\) \(\forall X,Y\in g_{-1}\). A Levi-Tanaka Lie algebra, which arises in the study of the group of pseudo-conformal automorphisms of a real submanifold \(M\) of a complex manifold \(X\) [cf. \textit{N. Tanaka}, J. Math. Kyoto Univ. 10, 1-82 (1970; Zbl 0206.50503)], is a graded real Lie algebra endowed with a partial complex structure satisfying certain (natural) conditions. In the article under review, the author gives a complete classification of the possible Levi-Tanaka algebra structures on real semisimple Lie algebras.
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 1463348
zbMATH Keywords: partial complex structure
zbMATH Keywords: graded real Lie algebra
zbMATH Keywords: Levi-Tanaka Lie algebra
zbMATH Keywords: real semisimple Lie algebras
reviewed by: Guangyu Shen
MaRDI profile type: Publication
cites work: Q3941610
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full work available at URL: https://doi.org/10.1007/bf01759376
OpenAlex ID: W1992493874
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description: scientific article; zbMATH DE number 1463348