33 citations · 270 across the 44 of their papers we have counts for
17 papers · 1 filter
Bipartite solutions of the set-theoretic Yang--Baxer equation
Gigel Militaru
We introduce a new class of unitary set-theoretic Yang--Baxter solutions, called \emph{bipartite} solutions. This class, which is purely combinatorial in nature, forms a full subca…
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…
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…
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…
Doi-Koppinen modules for quantum groupoids
Tomasz Brzezinski, Stefaan Caenepeel, Gigel Militaru
A definition of a Doi-Koppinen datum over a noncommutative algebra is proposed. The idea is to replace a bialgebra in a standard Doi-Koppinen datum with a bialgebroid. The correspo…
Bialgebroids, -bialgebras and duality
Tomasz Brzezinski, Gigel Militaru
An equivalence between Lu's bialgebroids, Xu's bialgebroids with an anchor and Takeuchi's -bialgebras is explicitly proven. A new class of examples of bialgebroids is c…
Heisenberg duoble, pentagon equation, structure and classification of finite dimensional Hopf algebras
G. Militaru
The study of the pentagon (fusion) equation leds to the Structure and the Classification theorem for finite dimenasional Hopf algebras: there exists a one to one correspondence bet…
Factorisation structures of algebras and coalgebras
S. Caenepeel, B. Ion, G. Militaru +1
We consider the factorisation problem for bialgebras: when a bialgebra factorises as , where and are algebras and coalgebras (but not necessarly bialgebras). Give…
A class of non-symmetric solutions for the integrability condition of the Knizhnik-Zamolodchikov equation: a Hopf algebra approach
Gigel Militaru
This paper studied what shall be called the Long equation: that is the system of nonlinear equation and . Any solution of th…
The Long dimodule category and nonlinear equation
Gigel Militaru
We study the Long dimodule category in conection with a nonlinear equation; we called the D-equation. The category of Long dimodules will play for the D-equation the same role as t…
New types of bialgebras arising from the Hopf equation
Gigel Militaru
New types of bialgebras arising from the Hopf equation (pentagonal equation) are introduced and studied. They will play from the Hopf equation the same role as the co-quasitriangul…
The Hopf modules category and the Hopf equation
Gigel Militaru
We study the Hopf equation which is equivalent to the pentagonal equation, from operator algebras. A FRT type theorem is given and new types of quantum groups are constructed. The…