Maximal abelian subalgebras of real and complex symplectic Lie algebras

DOI10.1063/1.525955zbMath0559.17005OpenAlexW2039980047MaRDI QIDQ5185223

Pavel Winternitz, Hans J. Zassenhaus, Jirí Patera

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1063/1.525955

zbMATH Keywords

classificationsymplectic Lie algebrasmaximal Abelian subalgebrasmaximal Abelian nilpotent algebras

Mathematics Subject Classification ID

Structure theory for Lie algebras and superalgebras (17B05) Applications of Lie groups to the sciences; explicit representations (22E70) Lie algebras of linear algebraic groups (17B45)

Related Items

HUYGENS' PRINCIPLE AND SEPARATION OF VARIABLES, Symmetry reduction for the Kadomtsev–Petviashvili equation using a loop algebra, Non-Hermitian superintegrable systems, The ABCD of topological recursion, The affinity of set theory and abelian group theory., Infinitesimally stable and unstable singularities of 2-degrees of freedom completely integrable systems, Maximal abelian subalgebras of pseudoorthogonal Lie algebras, On the symplectic structures in frame bundles and the finite dimension of basic symplectic cohomologies, Contractions of Lie algebras and separation of variables. The n-dimensional sphere, Maximal abelian subalgebras of pseudounitary Lie algebras, Maximal abelian subalgebras of complex orthogonal Lie algebras, Maximal abelian subalgebras of \(e(p,q)\) algebras, Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces, Solvable Leibniz Algebras with Heisenberg Nilradical, The minimal dimension of maximal commutative subalgebras of full matrix algebras

Cites Work

• Conjugacy classes in linear groups
• Separable coordinates for four-dimensional Riemannian spaces
• Conjugate classes of Cartan subalgebras in real semisimple Lie algebras
• Superposition principles for matrix Riccati equations
• Normal forms of elements of classical real and complex Lie and Jordan algebras
• Tensor fields invariant under subgroups of the conformal group of space-time
• Group actions on principal bundles and invariance conditions for gauge fields
• Quadratic Hamiltonians in phase space and their eigenstates
• Subgroups of Lie groups and separation of variables
• Complex orthogonal and symplectic matrices depending on parameters
• The maximal solvable subgroups of the SU(p,q) groups and all subgroups of SU(2,1)
• Subgroups of the Euclidean group and symmetry breaking in nonrelativistic quantum mechanics
• Subgroups of the Poincaré group and their invariants
• The maximal solvable subalgebras of the real classical Lie algebras
• Continuous subgroups of the fundamental groups of physics. III. The de Sitter groups
• The optical group and its subgroups
• Simple supersymmetries
• One-Parameter Subgroups of Unitary Groups with Indefinite Metric and in Particular of the Conformal Group
• ON MATRICES DEPENDING ON PARAMETERS
• ON THE CONJUGACY OF REAL CARTAN SUBALGEBRAS. I