8 citations · 9 across the 4 of their papers we have counts for
6 papers
Rank two Artin-Schelter regular algebras and non commuting derivations
Vincent Beck, César Lecoutre
If and are two derivations of a commutative algebra such that is locally nilpotent, one can endow with a new product whose filtered semiclassical l…
Rational equivalence for enveloping algebras of three-dimensional Lie algebras
Jacques Alev, François Dumas, César Lecoutre
We study from the point of view of rational equivalence the enveloping algebras of Lie algebras of dimension 3 whose derived Lie subalgebra is of dimension 2, over an algebraically…
On the semi-centre of a Poisson algebra
Cesar Lecoutre, Lewis Topley
If is a Lie algebra then the semi-centre of the Poisson algebra is the subalgebra generated by ad-eigenvectors. In this paper we ab…
A new family of Poisson algebras and their deformations
Cesar Lecoutre, Susan J. Sierra
Let be a field of characteristic zero. For any positive integer and any scalar , we construct a family of Artin-Schelter regular algebras , which are…
Poisson Deleting Derivations Algorithm and Poisson Spectrum
Stéphane Launois, César Lecoutre
In [5] Cauchon introduced the so-called deleting derivations algorithm. This algorithm was first used in noncommutative algebra to prove catenarity in generic quantum matrices, and…
A quadratic Poisson Gel'fand-Kirillov problem in prime characteristic
Stephane Launois, Cesar Lecoutre
The quadratic Poisson Gel'fand-Kirillov problem asks whether the field of fractions of a Poisson algebra is Poisson birationally equivalent to a Poisson affine space, i.e. to a pol…