77 citations · 535 across the 19 of their papers we have counts for
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Solvable Lie algebras with triangular nilradicals
Sébastien Tremblay, Pavel Winternitz
All finite-dimensional indecomposable solvable Lie algebras , having the triangular algebra T(n) as their nilradical, are constructed. The number of nonnilpotent elements $…
Bicomplex quantum mechanics: I. The generalized Schrödinger equation
Dominic Rochon, Sébastien Tremblay
We introduce the set of bicomplex numbers which is a commutative ring with zero divisors defined by $\mathbb{T}=\{w_0+w_1 \bold{i_1}+w_2\bold{i_2}+w_3 \bold{j}| w_0,w_…
Lie symmetries of multidimensional difference equations
Decio Levi, Sébastien Tremblay, Pavel Winternitz
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 o…
Invariants of the nilpotent and solvable triangular Lie algebras
Sébastien Tremblay, Pavel Winternitz
Invariants of the coadjoint representation of two classes of Lie algebras are calculated. The first class consists of the nilpotent Lie algebras , isomorphic to the algebras…
Lie point symmetries of difference equations and lattices
Decio Levi, Sébastien Tremblay, Pavel Winternitz
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 correspon…
Integrable systems without the Painlevé property
Alfred Ramani, Basile Grammaticos, Sébastien Tremblay
We examine whether the Painlevé property is a necessary condition for the integrability of nonlinear ordinary differential equations. We show that for a large class of linearisable…