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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

243 33

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.

402 29

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

72 17- PDF

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

117 11- PDF

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

117 10- PDF

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

49 10- PDF

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

108 9- PDF

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

302 8

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

181 7- PDF

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