79 citations · 180 across the 28 of their papers we have counts for
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On the Hopf envelope of finite-dimensional bialgebras
Alessandro Ardizzoni, Claudia Menini, Paolo Saracco
The Hopf envelope of a bialgebra is the free Hopf algebra generated by the given bialgebra. Its existence, as well as that of the cofree Hopf algebra, is a well-known fact in Hopf…
BiHom-Novikov algebras and infinitesimal BiHom-bialgebras
Ling Liu, Abdenacer Makhlouf, Claudia Menini +1
We introduce and study infinitesimal BiHom-bialgebras, BiHom-Novikov algebras, BiHom-Novikov-Poisson algebras, and find some relations among these concepts. Our main result is to s…
{sigma, tau}-Rota-Baxter operators, infinitesimal Hom-bialgebras and the associative (Bi)Hom-Yang-Baxter equation
Ling Liu, Abdenacer Makhlouf, Claudia Menini +1
We introduce the concept of {sigma, tau}-Rota-Baxter operator, as a twisted version of a Rota-Baxter operator of weight zero. We show how to obtain a certain {sigma, tau}-Rota-Baxt…
BiHom-pre-Lie algebras, BiHom-Leibniz algebras and Rota-Baxter operators on BiHom-Lie algebras
Ling Liu, Abdenacer Makhlouf, Claudia Menini +1
We investigate some properties of Rota-Baxter operators on BiHom-Lie algebras. Along the way, we introduce BiHom analogues of pre-Lie and Leibniz algebras.
Rota-Baxter operators on BiHom-associative algebras and related structures
Ling Liu, Abdenacer Makhlouf, Claudia Menini +1
The purpose of this paper is to study Rota-Baxter operators for BiHom-associative algebras. Moreover, we introduce and discuss the properties of the notions of BiHom-(tri)dendrifor…
Cohomology and Coquasi-bialgebras in the category of Yetter-Drinfeld Modules
Ivàn Angiono, Alessandro Ardizzoni, Claudia Menini
We prove that a finite-dimensional Hopf algebra with the dual Chevalley Property over a field of characteristic zero is quasi-isomorphic to a Radford-Majid bosonization whenever th…