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One of their most recent publications is **Lie algebras admitting non-singular prederivations**. Which was published in journal **Indagationes Mathematicae**.

More information about ** Ignacio Bajo** research including statistics on their citations can be found on their Copernicus Academic profile page.

AbstractThe aim of this paper is to prove that any real or complex Lie algebra admitting a non-singular prederivation is necessarily a nilpotent Lie algebra. As to the reciprocal statement, an example is given of a nilpotent Lie algebra with only singular prederivations.

AbstractWe study quadratic Lie algebras over a field K of null characteristic which admit, at the same time, a symplectic structure. We see that if K is algebraically closed every such Lie algebra may be constructed as the T∗-extension of a nilpotent Lie algebra admitting an invertible derivation and also as the double extension of another quadratic symplectic Lie algebra by the one-dimensional Lie algebra. Finally, we prove that every symplectic quadratic Lie algebra is a special symplectic Manin algebra and we give an inductive description in terms of symplectic quadratic double extensions.

AbstractWe study pulse accumulation phenomena in first order impulsive differential equations and give necessary and sufficient conditions to ensure pulse accumulation in such equations.

AbstractThe quadratic dimension of a Lie algebra is defined as the dimension of the linear space spanned by all its invariant non-degenerate symmetric bilinear forms. We prove that a quadratic Lie algebra with quadratic dimension equal to 2 is a local Lie algebra, this is to say, it admits a unique maximal ideal. We describe local quadratic Lie algebras using the notion of double extension and characterize those with quadratic dimension equal to 2 by the study of the centroid of such Lie algebras. We also give some necessary or sufficient conditions for a Lie algebra to have quadratic dimension equal to 2. Examples of local Lie algebras with quadratic dimension larger than 2 are given.

AbstractWe study the existence of invariant quadrics for a class of systems of difference equations in Rn defined by linear fractionals sharing denominator. Such systems can be described in terms of some square matrix A and we prove that there is a correspondence between non-degenerate invariant quadrics and solutions to a certain matrix equation involving A. We show that if A is semisimple and the corresponding system admits non-degenerate quadrics, then every orbit of the dynamical system is contained either in an invariant affine variety or in an invariant quadric.

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