5 papers
Poisson derivations and cohomology of Poisson nilpotent algebras
Stéphane Launois, Samuel Lopes, Isaac Oppong
We compute the Poisson derivations and the first Poisson cohomology group of uniparameter Poisson Nilpotent Algebras (PNA for short) under the hypothesis that Poisson-normal elemen…
Representations of compatible Lie algebras
Xabier GarcÃa-MartÃnez, Manuel Ladra, Bernardo Leite da Cunha +1
We study compatible Lie algebras from algebraic and representation-theoretic points of view, obtaining counterexamples to some fundamental theorems from classical Lie algebra theor…
Homological properties of some quantum Heisenberg algebras
Samuel A. Lopes, Héctor Suárez, Yésica Suárez
In this paper we study the properties Koszul, Artin-Schelter regular and (skew) Calabi-Yau of some special types of quantum and generalized Heisenberg algebras and also analyze rel…
Derivations and Hochschild cohomology of quantum nilpotent algebras
Stéphane Launois, Samuel A. Lopes, Isaac Oppong
We compute the derivations of Quantum Nilpotent Algebras under a technical (but necessary) assumption on the center. As a consequence, we give an explicit description of the first…
A classification of nilpotent compatible Lie algebras
Manuel Ladra, Bernardo Leite da Cunha, Samuel A. Lopes
Working over an arbitrary field of characteristic different from , we extend the Skjelbred-Sund method to compatible Lie algebras and give a full classification of nilpotent com…