27 citations · 50 across the 14 of their papers we have counts for
10 papers · 1 filter
On split regular Hom-Lie superalgebras
Helena Albuquerque, Elisabete Barreiro, Antonio J. Calderón +1
We introduce the class of split regular Hom-Lie superalgebras as the natural extension of the one of split Hom-Lie algebras and Lie superalgebras, and study its structure by showin…
The determinant, spectral properties, and inverse of a tridiagonal -Toeplitz matrix over a commutative ring
Jose Brox, Helena Albuquerque
A square matrix is -Toeplitz if its diagonals are periodic sequences of period . We find universal formulas for the determinant, the characteristic polynomial, some eigenvect…
Poisson algebras and symmetric Leibniz bialgebra structures on oscillator Lie algebras
Helena Albuquerque, Elisabete Barreiro, Saïd Benayadi +2
Oscillator Lie algebras are the only non commutative solvable Lie algebras which carry a bi-invariant Lorentzian metric. In this paper, we determine all the Poisson structures, and…
Leibniz superalgebras with a set grading
Helena Albuquerque, Elisabete Barreiro, Antonio J. Calderón +1
Consider a Leibniz superalgebra additionally graded by an arbitrary set (set grading). We show that decomposes as the sum of well-described graded i…
Split Lie-Rinehart algebras
Helena Albuquerque, Elisabete Barreiro, Antonio J. Calderón +1
We introduce the class of split Lie-Rinehart algebras as the natural extension of the one of split Lie algebras. We show that if is a tight split Lie-Rinehart algebra over an a…
Quasicrossed product on G-graded quasialgebras
Helena Albuquerque, Elisabete Barreiro, José M. Sánchez-Delgado
The notion of quasicrossed product is introduced in the setting of G-graded quasialgebras, i.e., algebras endowed with a grading by a group G, satisfying a "quasiassociative" law.…
Some (Hopf) algebraic properties of circulant matrices
Helena Albuquerque, Florin Panaite
We study some (Hopf) algebraic properties of circulant matrices, inspired by the fact that the algebra of circulant matrices is isomorphic to the group algebra of the c…
Alternative twisted tensor products and Cayley algebras
Helena Albuquerque, Florin Panaite
We introduce what we call "alternative twisted tensor products" for not necessarily associative algebras, as a common generalization of several different constructions: the Cayley-…
Quadratic Malcev Superalgebras with reductive even part
Helena Albuquerque, Elizabete Barreiro, Said Benayadi
It is our goal to give an inductive description of quadratic Malcev superalgebras with reductive even part. We use the notion of double extension of Malcev superalgebras presented…
Akivis Superalgebras and speciality
Helena Albuquerque, Ana Paula Santana
In this paper we define Akivis superalgebra and study enveloping superalgebras for this class of algebras, proving an analogous of the PBW Theorem. Lie and Malcev superalgebras are…