Zobrazeno 1 - 10
of 227
pro vyhledávání: '"Garcia Delgado R"'
Autor:
García-Delgado, R.
We state criteria for a nilpotent Lie algebra $\g$ to admit an invariant metric. We use that $\g$ possesses two canonical abelian ideals $\ide(\g) \subset \mathfrak{J}(\g)$ to decompose the underlying vector space of $\g$ and then we state sufficient
Externí odkaz:
http://arxiv.org/abs/2409.09017
Autor:
García-Delgado, R.
In this work we give an inductive way to construct quadratic Hom-Lie algebras with twist maps in the centroid. We focus on those Hom-Lie algebras that are not Lie algebras. We prove that the twist map of a Hom-Lie algebra of this type must be nilpote
Externí odkaz:
http://arxiv.org/abs/2409.04546
Autor:
García-Delgado, R.
In this work we state a result that relates the cohomology groups of a Lie algebra $\mathfrak{g}$ and a current Lie algebra $\mathfrak{g} \otimes \mathcal{S}$, by means of a short exact sequence -- similar to the universal coefficients theorem for mo
Externí odkaz:
http://arxiv.org/abs/2401.00553
Quadratic Hom-Lie algebras with equivariant twist maps are studied. They are completely characterized in terms of a maximal proper ideal that contains the kernel of the twist map and a complementary subspace to it that is either 1-dimensional, or has
Externí odkaz:
http://arxiv.org/abs/2304.06888
Hom-Lie algebras having non-invertible twist maps in their centroids are studied. Central extensions of Hom-Lie algebras having these properties are obtained and shown how the same properties are preserved. Conditions are given so that the produced c
Externí odkaz:
http://arxiv.org/abs/2212.13584
Autor:
García-Delgado, R.
In this work we state conditions for a current Lie algebra $\g \otimes \mathcal{S}$ to admit an invariant metric, where $\g$ is a quadratic Lie algebra and $\mathcal{S}$ is an associative and commutative algebra with unit. We also consider the recipr
Externí odkaz:
http://arxiv.org/abs/2208.14561
Publikováno v:
In Journal of Algebra 1 August 2024 651:221-242
Hom-Lie algebras defined on central extensions of a given quadratic Lie algebra that in turn admit an invariant metric, are studied. It is shown how some of these algebras are naturally equipped with other symmetric, bilinear forms that satisfy an in
Externí odkaz:
http://arxiv.org/abs/2010.06057
Autor:
García-Delgado, R.
In this work we state conditions on a covariant right exact functor so that it commutes with direct limits. These conditions are related to the commutativity of the functor under direct limits of projective modules. We prove that if the functor commu
Externí odkaz:
http://arxiv.org/abs/2006.03938
Solvable Lie algebras having at least one Abelian descending central ideal are studied. It is shown that all such Lie algebras can be built up from canonically defined ideals. The nature of such ideals is elucidated and their construction is provided
Externí odkaz:
http://arxiv.org/abs/1911.05009