Antonio Jesús Calderón

Decompositions of linear spaces induced by n-linear maps

Abstract Let be an arbitrary linear space and an n-linear map. It is proved that, for each choice of a basis of , the n-linear map f induces a (nontrivial) decomposition as a direct sum of linear subspaces of , with respect to . It is shown that this decomposition is f-orthogonal in the sense that when , and in such a way that any is strongly f-invariant, meaning that A sufficient condition for two different decompositions of induced by an n-linear map f, with respect to two different bases of , being isomorphic is deduced. The f-simplicity – an analog of the usual simplicity in the framework of n-linear maps – of any linear subspace of a certain decomposition induced by f is characterized. Finally, an application to the structure theory of arbitrary n-ary algebras is provided. This work is a close generalization the results obtained by Calderón.

n-Ary Generalized Lie-Type Color Algebras Admitting a Quasi-multiplicative Basis

The class of generalized Lie-type color algebras contains the ones of generalized Lie-type algebras, of n-Lie algebras and superalgebras, commutative Leibniz n-ary algebras and superalgebras, among others. We focus on the class of generalized Lie-type color algebras L

Arbitrary triple systems admitting a multiplicative basis

\frak L

The classification of 2-dimensional rigid algebras

admitting a quasi-multiplicative basis, with restrictions neither on the dimensions nor on the base field F

Poisson color algebras of arbitrary degree

\mathbb F

Leibniz algebras of Heisenberg type

and study its structure. We state that if L

On split regular Hom-Lie superalgebras

\frak L

The structure of split regular BiHom-Lie algebras ☆

admits a quasi-multiplicative basis then it decomposes as L=U⊕(∑Jk)

Classification of bilinear maps with radical of codimension 2

\mathfrak {L} ={\mathcal U} \oplus (\sum \limits {\frak J}_{k})

The classification of

with any Jk