Nonlinear equations with superposition formulas and the exceptional group G2. I. Complex and real forms of g2 and their maximal subalgebras

DOI10.1063/1.526993zbMath0614.22008OpenAlexW1997496854MaRDI QIDQ4722271

Véronique Hussin, Jules Beckers, Pavel Winternitz

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1063/1.526993

zbMATH Keywords

invariant subspacesfundamental representationnonlinear ordinary differential equationsexceptional simple Lie groupparabolic subalgebrassuperposition principlesmaximal subalgebras\(G_ 2\)matrix realizations

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Nonlinear differential equations in abstract spaces (34G20) Exceptional (super)algebras (17B25) Analysis on real and complex Lie groups (22E30) Applications of Lie groups to the sciences; explicit representations (22E70) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65)

Related Items (9)

Geometrical applications of split octonions ⋮ A geometric approach to time evolution operators of Lie quantum systems ⋮ Rotations in the space of Split octonions ⋮ The matrix representations of g2. I. Representations in an so(4) basis ⋮ Nonlinear equations with superposition formulas and exceptional group G2. III. The superposition formulas ⋮ Group theoretical approach to the intertwined Hamiltonians ⋮ Nonlinear equations with superposition formulas and the exceptional group G2. II. Classification of the equations ⋮ OCTONIONIC VERSION OF DIRAC EQUATIONS ⋮ Quasi-Lie schemes for PDEs

Cites Work

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• Continuous subgroups of the fundamental groups of physics. III. The de Sitter groups
• Direct determination of the Langlands decompositions for the parabolic subalgebras of noncompact semisimple real Lie algebras
• Theory of Complex Spectra. IV

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