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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

Invariants of the nilpotent and solvable triangular Lie algebras

- S. Tremblay, P. Winternitz
- Mathematics, Physics
- 12 October 2001

Invariants of the coadjoint representation of two classes of Lie algebras are calculated. The first class consists of the nilpotent Lie algebras T(M), isomorphic to the algebras of upper triangular… Expand

Integrable lattice equations and their growth properties

- S. Tremblay, B. Grammaticos, A. Ramani
- Physics, Mathematics
- 15 January 2001

Abstract In this Letter we investigate the integrability of two-dimensional partial difference equations using the newly developed techniques of study of the degree of the iterates. We show that… Expand

Bicomplex Quantum Mechanics: II. The Hilbert Space

- D. Rochon, S. Tremblay
- Mathematics, Physics
- 26 October 2005

Abstract.Using the bicomplex numbers
$$ \mathbb{T} \cong {\hbox{Cl}}_{\mathbb{C}} (1,0) \cong {\hbox{Cl}}_{\mathbb{C}} (0,1) $$ which is a commutative ring with zero divisors defined by
$$ \mathbb{T}… Expand

Complete systems of recursive integrals and Taylor series for solutions of Sturm–Liouville equations

- V. Kravchenko, Samy Morelos, S. Tremblay
- Mathematics
- 27 March 2011

Given a regular nonvanishing complex valued solution y0 of the equation , x ∈ (a,b), assume that it is n times differentiable at a point x0 ∈ [a,b]. We present explicit formulas for calculating the… Expand

Lie point symmetries of difference equations and lattices

- D. Levi, S. Tremblay, P. Winternitz
- Mathematics, Physics
- 1 December 2000

A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference… Expand

Fine grading of sl(p2,C) generated by tensor product of generalized Pauli matrices and its symmetries

- E. Pelantová, Milena Svobodová, S. Tremblay
- Physics, Mathematics
- 13 October 2005

Study of the normalizer of the MAD-group corresponding to a fine grading offers the most important tool for describing symmetries in the system of nonlinear equations connected with contraction of a… Expand

Bicomplex Quantum Mechanics: I. The Generalized Schrödinger Equation

- D. Rochon, S. Tremblay
- Mathematics, Physics
- 1 October 2004

Abstract.We introduce the set of bicomplex numbers
$$\mathbb{T}$$ which is a commutative ring with zero divisors defined by
$$\mathbb{T} = \{ \omega _0 + \omega _1 {\mathbf{i}}_{\mathbf{1}} + \omega… Expand

Wave polynomials, transmutations and Cauchy’s problem for the Klein–Gordon equation

- K. Khmelnytskaya, V. Kravchenko, S. Torba, S. Tremblay
- Mathematics, Physics
- 29 August 2012

Abstract We prove a completeness result for a class of polynomial solutions of the wave equation called wave polynomials and construct generalized wave polynomials, solutions of the Klein–Gordon… Expand

Lie symmetries of multidimensional difference equations

- D. Levi, S. Tremblay, P. Winternitz
- Mathematics, Physics
- 9 November 2001

A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They… Expand

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