33 citations · 270 across the 44 of their papers we have counts for
24 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…
Crossed products of -algebras. Applications
G. Militaru
A -algebra is a commutative algebra over a field such that , for all . We have proved recently \cite{Mil} that -algebras play a prominent role i…
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…
The automorphisms group and the classification of gradings of finite dimensional associative algebras
G. Militaru
Let be an -dimensional algebra over a field and its quantum symmetry semigroup. We prove that the automorphisms group of is isomorph…
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…
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…
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…
Metabelian associative algebras
G. Militaru
Metabelian algebras are introduced and it is shown that an algebra is metabelian if and only if is a nilpotent algebra having the index of nilpotency at most , i.e. $x y…
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…
The global extension problem, co-flag and metabelian Leibniz algebras
Gigel Militaru
Let be a Leibniz algebra, a vector space and an epimorphism of vector spaces with . The global extension p…
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…
Four problems regarding representable functors
Gigel Militaru
Let , be two rings, an -coring and the category of left -comodules. The category …
Serre Theorem for involutory Hopf algebras
G. Militaru
We call a monoidal category a Serre category if for any , such that $C\ot D$ is semisimple, and are semisimple objects in ${\mathcal…
Naturally full functors in nature
A. Ardizzoni, S. Caenepeel, C. Menini +1
We introduce and discuss the notion of naturally full functor. The definition is similar to the definition of separable functor: a naturally full functor is a functorial version of…
Maschke functors, semisimple functors and separable functors of the second kind. Applications
S. Caenepeel, G. Militaru
We introduce separable functors of the second kind (or -separable functors) and -Maschke functors. -separable functors are generalizations of separable functors. Various n…
Frobenius Functors of the second kind
S. Caenepeel, E. De Groot, G. Militaru
A pair of adjoint functors is called a Frobenius pair of the second type if is a left adjoint of for some category equivalences and . Frobenius ring extens…
Frobenius and Mashke type Theorems for Doi-Hopf modules and entwined modules revisited: a unified approach
Tomasz Brzezinski, S. Caenepeel, G. Militaru +1
We study when induction functors (and their adjoints) between categories of Doi-Hopf modules and, more generally, entwined modules are separable, resp. Frobenius. We present a unif…