48 citations · 172 across the 35 of their papers we have counts for
6 papers · 1 filter
Preantipodes for dual-quasi bialgebras
Alessandro Ardizzoni, Alice Pavarin
It is known that a dual quasi-bialgebra with antipode , i.e. a dual quasi-Hopf algebra, fulfils a fundamental theorem for right dual quasi-Hopf -bicomodules. The converse in…
Gauge deformations for Hopf algebras with the dual Chevalley property
Alessandro Ardizzoni, Margaret Beattie, Claudia Menini
Let be a Hopf algebra over a field of characteristic zero such that its coradical is a finite dimensional sub-Hopf algebra. Our main theorem shows that there is a gauge…
Cocycle deformations for liftings of quantum linear spaces
Alessandro Ardizzoni, Margaret Beattie, Claudia Menini
Let be a Hopf algebra over a field of characteristic 0 and suppose there is a coalgebra projection from to a sub-Hopf algebra that splits the inclusion. If the…
Universal Enveloping Algebras of PBW Type
Alessandro Ardizzoni
We continue our investigation of the general notion of universal enveloping algebra introduced in [A. Ardizzoni, \emph{A Milnor-Moore Type Theorem for Primitively Generated Braided…
Categories of comodules and chain complexes of modules
A. Ardizzoni, L. El Kaoutit, C. Menini
Let $\lL(A)$ denote the coendomorphism left -bialgebroid associated to a left finitely generated and projective extension of rings with identities. We show that the ca…
A Milnor-Moore Type Theorem for Primitively Generated Braided Bialgebras
Alessandro Ardizzoni
A braided bialgebra is called primitively generated if it is generated as an algebra by its space of primitive elements. We prove that any primitively generated braided bialgebra i…