4 papers
Generalized NS-algebras
Cyrille Ospel, Florin Panaite, Pol Vanhaecke
We generalize to arbitrary categories of algebras the notion of an NS-algebra. We do this by using a bimodule property, as we did for defining the general notions of a dendriform a…
Polarization and deformations of generalized dendriform algebras
Cyrille Ospel, Florin Panaite, Pol Vanhaecke
We generalize three results of M. Aguiar, which are valid for Loday's dendriform algebras, to arbitrary dendriform algebras, i.e., dendriform algebras associated to algebras satisf…
Poisson enveloping algebras and the Poincaré-Birkhoff-Witt theorem
Thierry Lambre, Cyrille Ospel, Pol Vanhaecke
Poisson algebras are, just like Lie algebras, particular cases of Lie-Rinehart algebras. The latter were introduced by Rinehart in his seminal 1963 paper, where he also introduces…
Cohomological properties of the quantum shuffle product and application to the construction of quasi-Hopf algebras
Cyrille Ospel
For a commutative algebra the shuffle product is a morphism of complexes. We generalize this result to the quantum shuffle product, associated to a class of non-commutative algebra…