A study of the reducibility of the Fock space representation of the q-deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is carried out by using the properties of the Gauss ...

A study of the reducibility of the Fock space representation of the q-deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is carried out by using the properties of the Gauss ...

We begin the study of PBW deformations of graded algebras relevant to the theory of Hopf algebras. One of our examples is the Fomin–Kirillov algebra E3. Another one appeared in a paper of García Iglesias and Vay. As a ...

We exhibit the first example of a non-rigid complex filiform Lie algebra with all its codimension 1 ideals being characteristically nilpotent by constructing an explicit nontrivial filiform deformation of it.

In this article we establish an explicit link between the classical theory of deformations à la Gerstenhaber (and a fortiori with the Hochschild cohomology) and (weak) PBW-deformations of homogeneous algebras. Our point ...

We apply the Nash–Moser theorem for exact sequences of R. Hamilton to the context of deformations of Lie algebras and we discuss some aspects of the scope of this theorem in connection with the polynomial ideal associated ...