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- Publications
- Influence
Subalgebras of real three‐ and four‐dimensional Lie algebras
- J. Patera, P. Winternitz
- Mathematics
- 1 July 1977
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 are… Expand
Invariants of real low dimension Lie algebras
- J. Patera, R. Sharp, P. Winternitz, H. Zassenhaus
- Mathematics
- 1 June 1976
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.
Classification and Identification of Lie Algebras
- L. Šnobl, P. Winternitz
- Mathematics
- 26 February 2014
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 the… Expand
Superintegrable systems in Darboux spaces
- E. Kalnins, J. Kress, W. Miller, P. Winternitz
- Mathematics, Physics
- 18 July 2003
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 of… Expand
Continuous subgroups of the fundamental groups of physics. II. The similitude group
- J. Patera, P. Winternitz, H. Zassenhaus
- Mathematics
- 1 August 1975
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 made… Expand
Solvable Lie algebras with triangular nilradicals
- S. Tremblay, P. Winternitz
- Mathematics, Physics
- 16 January 1998
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 the… Expand
FAST TRACK COMMUNICATION: An infinite family of solvable and integrable quantum systems on a plane
- F. Tremblay, A. Turbiner, P. Winternitz
- Mathematics, Physics
- 4 April 2009
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 of… Expand
Non-classical symmetry reduction: example of the Boussinesq equation
- D. Levi, P. Winternitz
- Mathematics
- 7 August 1989
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 authors… Expand
Classical and quantum superintegrability with applications
- W. Miller, S. Post, P. Winternitz
- Mathematics, Physics
- 10 September 2013
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 quantum… Expand
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