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Subalgebras of real three‐ and four‐dimensional Lie algebras
The Lie subalgebras of all real Lie algebras of dimension d?4 are classified into equivalence classes under their groups of inner automorphisms. Tables of representatives of each conjugacy class areExpand
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Invariants of real low dimension Lie algebras
All invariant functions of the group generators (generalized Casimir operators) are found for all real algebras of dimension up to five and for all real nilpotent algebras of dimension six.
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Classification and Identification of Lie Algebras
The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address theExpand
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Superintegrable systems in Darboux spaces
Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four Darboux spaces ofExpand
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Continuous subgroups of the fundamental groups of physics. II. The similitude group
All subalgebras of the similitude algebra (the algebra of the Poincare group extended by dilatations) are classified into conjugacy classes under transformations of the similitude group. Use is madeExpand
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Solvable Lie algebras with triangular nilradicals
All finite-dimensional indecomposable solvable Lie algebras , having the triangular algebra T(n) as their nilradical, are constructed. The number of non-nilpotent elements f in satisfies and theExpand
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FAST TRACK COMMUNICATION: An infinite family of solvable and integrable quantum systems on a plane
An infinite family of exactly solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing separation ofExpand
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Non-classical symmetry reduction: example of the Boussinesq equation
A symmetry of an equation will leave the set of all solutions invariant. A 'conditional symmetry' will leave only a subset of solutions, defined by some differential condition, invariant. The authorsExpand
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Classical and quantum superintegrability with applications
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantumExpand
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