33 citations · 238 across the 41 of their papers we have counts for
14 papers · 1 filter
Płonka bi-magmas and the set-theoretic Yang--Baxter equation
A. L. Agore, A. Chirvasitu, G. Militaru
We introduce a new variety of universal algebras with two binary operations, called \emph{Płonka bi-magmas}, and use them to construct novel solutions to the set-theoretic Yang-Bax…
The set-theoretic Yang-Baxter equation, Kimura semigroups and functional graphs
A. L. Agore, A. Chirvasitu, G. Militaru
We prove that the category of solutions of the set-theoretic Yang-Baxter equation of Frobenius-Separability (FS) type is equivalent to the category of pointed Kimura semigroups. As…
Universal coacting Poisson Hopf algebras
A. L. Agore
We introduce the analogue of Manin's universal coacting (bialgebra) Hopf algebra for Poisson algebras. First, for two given Poisson algebras and , where is finite dimens…
Constructing Hopf braces
A. L. Agore
We investigate Hopf braces, a concept recently introduced by Angiono, Galindo and Vendramin in connection to the quantum Yang-Baxter equation. More precisely, we propose two method…
The uniqueness of braidings on the monoidal category of non-commutative descent data
A. L. Agore, S. Caenepeel, G. Militaru
Let be an algebra over a commutative ring . It is known that the categories of non-commutative descent data, of comodules over the Sweedler canonical coring, of right -mo…
Classifying coalgebra split extensions of Hopf algebras
A. L. Agore, C. G. Bontea, G. Militaru
For a given Hopf algebra we classify all Hopf algebras that are coalgebra split extensions of by , where is the Sweedler's 4-dimensional Hopf algebra. Equiva…
Classifying complements for Hopf algebras and Lie algebras
A. L. Agore, G. Militaru
Let be a given extension of Hopf (respectively Lie) algebras. We answer the \emph{classifying complements problem} (CCP) which consists of describing and classifyin…
Classifying bicrossed products of Hopf algebras
A. L. Agore, C. G. Bontea, G. Militaru
Let and be two Hopf algebras. We shall classify up to an isomorphism that stabilizes all Hopf algebras that factorize through and by a cohomological type ob…
Coquasitriangular structures for extensions of Hopf algebras. Applications
A. L. Agore
Let be an extension of Hopf algebras such that there exists a normal left -module coalgebra map that splits the inclusion. We shall describe the set…
Crossed product of Hopf algebras
A. L. Agore
The main properties of the crossed product in the category of Hopf algebras are investigated. Let and be two Hopf algebras connected by two morphism of coalgebras $\triangl…
The center of the category of bimodules and descent data for non-commutative rings
A. L. Agore, S. Caenepeel, G. Militaru
Let be an algebra over a commutative ring . We compute the center of the category of -bimodules. There are six isomorphic descriptions: the center equals the weak center,…
Braidings on the category of bimodules, Azumaya algebras and epimorphisms of rings
A. L. Agore, S. Caenepeel, G. Militaru
Let be an algebra over a commutative ring . We prove that braidings on the category of -bimodules are in bijective correspondence to canonical R-matrices, these are eleme…
Limits of Coalgebras, Bialgebras and Hopf Algebras
A. L. Agore
We give the explicit construction of the product of an arbitrary family of coalgebras, bialgebras and Hopf algebras: it turns out that the product of an arbitrary family of coalgeb…
Categorical Constructions for Hopf Algebras
A. L. Agore
We prove that both, the embedding of the category of Hopf algebras into that of bialgebras and the forgetful functor from the category of Hopf algebras to the category of algebras,…