On covariant realizations of the Poincaré group \(P(1,3)\)
type: Item
instance of: scholarly article
title: On covariant realizations of the Poincaré group \(P(1,3)\)
zbMATH Open document ID: 1044.81057
DOI: 10.1016/S0034-4877(02)80054-4
author: Maxim Lutfullin
published in: Reports on Mathematical Physics
publication date: 2003-10-07T00:00:00Z
review text: The author describes realizations of the Poincaré Lie algebra \(p = so(1,3) +\mathbb R^{1,3}\) in the space \(\mathbb R^{1,3} \times \mathbb C^n\) which are extensions of the standard action of \(p\) on the Minkowski space \(\mathbb R^{1,3}\) with the trivial action of the translation subalgebra \(\mathbb R^{1,3} \) on \(\mathbb C^n\). The problem reduces to the construction of realisations of the Lorentz Lie algebra \(so(1,3)\) by holomorphic vector fields on \(\mathbb C^n\) up to a bi-holomorphic transformations. All such realisations are described, using the fact that the complexification of the Lorentz Lie algebra is a direct sum of two copies of \(sl(2,\mathbb C)\).
Mathematics Subject Classification ID: 81R05
Mathematics Subject Classification ID: 22E43
Mathematics Subject Classification ID: 22E70
zbMATH DE Number: 1947245
zbMATH Keywords: Poincaré group
zbMATH Keywords: realization of Lie algebras by vector fields
reviewed by: Dmitri Alekseevsky
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1947245