70 citations · 85 across the 8 of their papers we have counts for
8 papers
Bicomplex Algebraic Numbers
Hichem Gargoubi, Sayed Kossentini
We investigate bicomplex analogues of fundamental notions from classical algebraic number theory. In particular, we show that the primitive element theorem admits a natural general…
Bicomplex numbers as a normal complexified f-algebra
Hichem Gargoubi, Sayed Kossentini
The algebra B of bicomplex numbers is viewed as a complexification of the Archimedean f-algebra of hyperbolic numbers D. This lattice-theoretic approach allows us to establish new…
Supertransvectants and symplectic geometry
Hichem Gargoubi, Valentin Ovsienko
We consider the -invariant bilinear operations on weighted densities on the supercircle called the supertransvectants. These operations are analogues of the fam…
Differential operators on supercircle: conformally equivariant quantization and symbol calculus
Hichem Gargoubi, Najla Mellouli, Valentin Ovsienko
We consider the supercircle equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on as the Lie superalgebra of contact vector…
Symmetries of modules of differential operators
Hichem Gargoubi, Pierre Mathonet, Valentin Ovsienko
Let be the space of tensor densities of degree (or weight) on the circle . The space of -th order linear differential operat…
Algebra gl(λ) inside the algebra of differential operators on the real line
Hichem Gargoubi
The Lie algebra gl(λ) with λ\in \mathbb C, introduced by B.L.Feigin, can be embedded into the Lie algebra of differential operators on the real line. We give an explicit formula of…