43 citations · 100 across the 18 of their papers we have counts for
10 papers · 1 filter
Structure and isomorphisms of quantum generalized Heisenberg algebras
Samuel A. Lopes, Farrokh Razavinia
In [14] we introduced a new class of algebras, which we named \textit{quantum generalized Heisenberg algebras} and which depend on a parameter and two polynomials . We hav…
Non-associative central extensions of null-filiform associative algebras
Ivan Kaygorodov, Samuel A. Lopes, Pilar Páez-Guillán
We give the algebraic classification of alternative, left alternative, Jordan, bicommutative, left commutative, assosymmetric, Novikov and left symmetric central extensions of null…
The algebraic and geometric classification of nilpotent anticommutative algebras
Ivan Kaygorodov, Mykola Khrypchenko, Samuel A. Lopes
We give algebraic and geometric classifications of -dimensional complex nilpotent anticommutative algebras. Specifically, we find that, up to isomorphism, there are one-par…
Degenerations of nilpotent associative commutative algebras
Ivan Kaygorodov, Samuel A. Lopes, Yury Popov
We give a complete description of degenerations of complex -dimensional nilpotent associative commutative algebras.
Non-Noetherian generalized Heisenberg algebras
Samuel A. Lopes
In this note we classify the non-Noetherian generalized Heisenberg algebras H(f) introduced by Rencai Lü and Kaiming Zhao [Linear Algebra Appl., 2015]. In case the polynomial f has…
A Parametric Family of Subalgebras of the Weyl Algebra III. Derivations
Georgia Benkart, Samuel A. Lopes, Matthew Ondrus
An Ore extension over a polynomial algebra F[x] is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra A_h generated by elements x…
A Parametric Family of Subalgebras of the Weyl Algebra I. Structure and Automorphisms
Georgia Benkart, Samuel A. Lopes, Matthew Ondrus
An Ore extension over a polynomial algebra is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra g…
Classification of factorial generalized down-up algebras
Stéphane Launois, Samuel A. Lopes
We determine when a generalized down-up algebra is a Noetherian unique factorisation domain or a Noetherian unique factorisation ring.
Double Ore Extensions versus Iterated Ore Extensions
Paula A. A. B. Carvalho, Samuel A. Lopes, Jerzy Matczuk
Motivated by the construction of new examples of Artin-Schelter regular algebras of global dimension four, J.J. Zhang and J. Zhang (2008) introduced an algebra extension $A_P[y_1,y…
Automorphisms of Generalized Down-Up Algebras
Paula A. A. B. Carvalho, Samuel A. Lopes
A generalization of down-up algebras was introduced by Cassidy and Shelton (J. Algebra 279 (2004), no. 1), the so-called generalized down-up algebras. We describe the automorphism…