33 citations · 238 across the 41 of their papers we have counts for
20 papers · 1 filter
Universal constructions for Poisson algebras. Applications
A. L. Agore, G. Militaru
We introduce the \emph{universal algebra} of two Poisson algebras and as a commutative algebra satisfying a certain universal property. The uni…
Functors between representation categories. Universal modules
A. L. Agore
Let and be two Lie algebras with finite dimensional and consider to be th…
The factorization problem for Jordan algebras. Applications
A. L. Agore, G. Militaru
We investigate the factorization problem as well as the classifying complements problem in the setting of Jordan algebras. Matched pairs of Jordan algebras and the corresponding bi…
Unified products for Jordan algebras. Applications
A. L. Agore, G. Militaru
Given a Jordan algebra and a vector space , we describe and classify all Jordan algebras containing as a subalgebra of codimension in terms of a non-ab…
A new invariant for finite dimensional Leibniz/Lie algebras
A. L. Agore, G. Militaru
For an -dimensional Leibniz/Lie algebra over a field we introduce a new invariant , called the \emph{universal algebra} of $\mathf…
-universal Hopf algebras (co)acting on -algebras
Ana Agore, Alexey Gordienko, Joost Vercruysse
We develop a theory which unifies the universal (co)acting bi/Hopf algebras as studied by Sweedler, Manin and Tambara with the recently introduced \cite{AGV1} bi/Hopf-algebras that…
Equivalences of (co)module algebra structures over Hopf algebras
Ana Agore, Alexey Gordienko, Joost Vercruysse
We introduce the notion of support equivalence for (co)module algebras (over Hopf algebras), which generalizes in a natural way (weak) equivalence of gradings. We show that for eac…
Hopf Algebras which Factorize through the Taft Algebra and the Group Hopf Algebra
Ana-Loredana Agore
We completely describe by generators and relations and classify all Hopf algebras which factorize through the Taft algebra and the group Hopf algebra : the…
On a type of commutative algebras
A. L. Agore, G. Militaru
We introduce some basic concepts for Jacobi-Jordan algebras such as: representations, crossed products or Frobenius/metabelian/co-flag objects. A new family of solutions for the qu…
Galois groups and group actions on Lie algebras
A. L. Agore, G. Militaru
If is an extension of Lie algebras over a field such that and , then…
The maximal dimension of unital subalgebras of the matrix algebra
A. L. Agore
Using Wederburn's main theorem and a result of Gerstenhaber we prove that, over a field of characteristic zero, the maximal dimension of a proper unital subalgebra in the $n \times…
Itô's theorem and metabelian Leibniz algebras
A. L. Agore, G. Militaru
We prove that the celebrated Itô's theorem for groups remains valid at the level of Leibniz algebras: if is a Leibniz algebra such that , for t…
Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras
Ana-Loredana Agore, Gigel Militaru
For a perfect Lie algebra we classify all Lie algebras containing as a subalgebra of codimension . The automorphism groups of such Lie algebras are…
The global extension problem, crossed products and co-flag non-commutative Poisson algebras
A. L. Agore, G. Militaru
Let be a Poisson algebra, a vector space and an epimorphism of vector spaces with . The global extension problem asks for the classification…
Unified products for Leibniz algebras. Applications
A. L. Agore, G. Militaru
Let be a Leibniz algebra and a vector space containing as a subspace. All Leibniz algebra structures on containing as a subalge…
Extending structures for Lie algebras
A. L. Agore, G. Militaru
Let be a Lie algebra, a vector space containing as a subspace. The paper is devoted to the \emph{extending structures problem} which asks for the…
The Classification of All Crossed Products
Ana-Loredana Agore, Costel-Gabriel Bontea, Gigel Militaru
Using the computational approach introduced in [Agore A.L., Bontea C.G., Militaru G., J. Algebra Appl. 12 (2013), 1250227, 24 pages, arXiv:1207.0411] we classify all coalgebra spli…
Unified products and split extensions of Hopf algebras
A. L. Agore, G. Militaru
The unified product was defined in \cite{am3} related to the restricted extending structure problem for Hopf algebras: a Hopf algebra factorizes through a Hopf subalgebra a…
Extending Structures II: The Quantum Version
A. L. Agore, G. Militaru
Let A be a Hopf algebra and H a coalgebra. We shall describe and classify up to an isomorphism all Hopf algebras E that factorize through A and H: that is E is a Hopf algebra such…
Monomorphisms of Coalgebras
A. L. Agore
We prove new necessary and sufficient conditions for a morphism of coalgebras to be a monomorphism, different from the ones already available in the literature. More precisely, $ϕ:…