An embedding of the Poincaré Lie algebra into an extension of the Lie field of SO0(1,4)

DOI10.1063/1.530307zbMath0807.22011OpenAlexW2042935898WikidataQ115331020 ScholiaQ115331020MaRDI QIDQ4276768

Patrick Moylan, Miloslav Havlíček

Publication date: 17 November 1994

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530307

zbMATH Keywords

Poincaré groupenergy representationsPoincaré Lie algebraunitary ray representationsLie fields of \(\text{SO}_ 0 (1,4)\)

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Lie algebras of vector fields and related (super) algebras (17B66) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70) Structure and representation of the Lorentz group (22E43)

Related Items

Representations of the Poincaré Lie algebra from unitary representations of SO(1,4), Construction of representations of Poincaré group using Lie fields, Tachyons and Representations of "Equation missing", Localizations of $$ U_{q}(\mathfrak{s}\mathfrak{l}(2))$$ and $$ U_{q}(\mathfrak{o}\mathfrak{s}\mathfrak{p}(1\vert 2))$$ Associated with Euclidean and Super Euclidean Algebras

Cites Work

• A note on the representations of the De Sitter group
• On the integrability of certain symmetric representations of the Lie algebra of SO0(4,1)
• Unitary representations of the (4+1)-de Sitter group on irreducible representation spaces of the Poincaré group
• Gell-Mann formula for simple complex Lie groups and geometric quantization
• Eigenspaces of the Laplace-Beltrami operator on a hyperboloid
• Group contraction in a fiber bundle with Cartan connection
• Zur Darstellungstheorie der inhomogenen Lorentzgruppe als Grundlage quantenmechanischer Kinematik
• Decompositions of Discrete Most Degenerate Representations of SO(p, q) when Restricted to Representations of SO(p, q − 1) or SO(p − 1, q)
• On the supplementary series of SO0(p, 1)
• Group Theoretical Discussion of Relativistic Wave Equations