arXiv subjects

Nadina Elizabeth Rojas

Publications and source records attributed to Nadina Elizabeth Rojas.

5 recordsLinked to original sources

arXiv2023

Classification of orbit closures in the variety of 4-dimensional symplectic Lie algebras

The aim of this paper is to study the natural action of the real symplectic group, $\operatorname{Sp}(4, \mathbb{R})$, on the algebraic set of $4$-dimensional Lie algebras admitting symplectic structures and to give a complete classification of orbit closures. We present some applications of such classification to the study of the Ricci curvature of left-invariant almost Kähler structures on four dimensional Lie groups.

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arXiv2019

On the classification of $3$-dimensional complex hom-Lie algebras

We classify hom-Lie structures with nilpotent twisting map on $3$-dimensional complex Lie algebras, up to isomorphism, and classify all degenerations in such family. The ideas and techniques presented here can be easily extrapolated to study similar problems in other algebraic structures and provide different perspectives from where one can tackle classical open problems of interest in rigid Lie algebras.

math.RA↗

arXiv2018

The Automorphisms group of a Current Lie algebra

Let $\mathfrak{g}$ be a finite dimensional complex Lie algebra and let $A$ be a finite dimensional complex, associative and commutative algebra with unit. We describe the structure of the derivation Lie algebra of the current Lie algebra $\mathfrak{g}_A= \mathfrak{g} \otimes A$, denoted by $\operatorname{Der}(\mathfrak{g}_A)$. Furthermore, we obtain the Levi decomposition of $\operatorname{Der}(\mathfrak{g}_A)$. As a consequence of the last result, if $\mathfrak{h}_m$ is the Heisenberg Lie algebra of dimension $2 m + 1$, we obtain a faithful representation of $\operatorname{Der}(\mathfrak{h}_{m,k})$ of the current truncated Heisenberg Lie algebra $\mathfrak{h}_{m,k}= \mathfrak{h}_m \otimes \mathbb{C}[t]/ (t^{k + 1})$ for all positive integer $k$.

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arXiv2012

Minimal Faithful Representation of the Heisenberg Lie Algebra with Abelian Factor

For a finite dimensional Lie algebra $\g$ over a field $\k$ of characteristic zero, the $μ$-function (respectively $μ_{nil}$-function) is defined to be the minimal dimension of $V$ such that $\g$ admits a faithful representation (respectively a faithful nilrepresentation) on $V$. Let $\h_m$ be the Heisenberg Lie algebra of dimension $2m + 1$ and let $\mathfrak{a}_n$ be the abelian Lie algebra of dimension $n$. The aim of this paper is to compute $μ(\h_m \oplus \mathfrak{a}_n)$ and $μ_{nil}(\h_m \oplus \mathfrak{a}_n)$ for all $m,n \in \mathbb{N}$.

math.RT↗

arXiv2012

Faithful Representations of Minimal Dimension of 6-dimensional nilpotent Lie algebras

The main goal of this paper is to compute $μ(\g)$ and $μ_{nil}(\g)$ for each nilpotent Lie algebra $\g$ of dimension 6 over a field of characteristic zero $\k$. Here $μ(\g)$ and $μ_{nil}(\g)$ is the minimal dimension of a faithful representation of $\g$ and the minimal dimension of a faithful nilrepresentation of $\g$, respectively. We also give a minimal faithful representation and nilrepresentation for each nilpotent Lie algebra of dimension $\leq 6$.

math.RT↗