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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
Invariants of the nilpotent and solvable triangular Lie algebras
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 triangularExpand
Integrable lattice equations and their growth properties
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 thatExpand
Bicomplex Quantum Mechanics: II. The Hilbert Space
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 $$ \mathbb{T}Expand
Complete systems of recursive integrals and Taylor series for solutions of Sturm–Liouville equations
Given a regular nonvanishing complex valued solution y0 of the equation , x ∈ (a,b), assume that it is n times differentiable at a point x0 ∈ [a,b]. We present explicit formulas for calculating theExpand
Lie point symmetries of difference equations and lattices
A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding differenceExpand
Fine grading of sl(p2,C) generated by tensor product of generalized Pauli matrices and its symmetries
Study of the normalizer of the MAD-group corresponding to a fine grading offers the most important tool for describing symmetries in the system of nonlinear equations connected with contraction of aExpand
Bicomplex Quantum Mechanics: I. The Generalized Schrödinger Equation
Abstract.We introduce the set of bicomplex numbers $$\mathbb{T}$$ which is a commutative ring with zero divisors defined by $$\mathbb{T} = \{ \omega _0 + \omega _1 {\mathbf{i}}_{\mathbf{1}} + \omegaExpand
Wave polynomials, transmutations and Cauchy’s problem for the Klein–Gordon equation
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–GordonExpand
Lie symmetries of multidimensional difference equations
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. TheyExpand