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pro vyhledávání: '"17B30"'
A Riemannian manifold is called \emph{weakly Einstein} if the tensor $R_{iabc}R_{j}^{~~abc}$ is a scalar multiple of the metric tensor $g_{ij}$. We consider weakly Einstein Lie groups with a left-invariant metric which are weakly Einstein. We prove t
Externí odkaz:
http://arxiv.org/abs/2411.12311
Autor:
García-Delgado, R.
In this work we state a version of the double extension for homogeneous quadratic Lie super algebras that includes even and odd cases. We prove that any indecomposable, non-simple and homogeneous quadratic Lie super algebra is obtained by means of th
Externí odkaz:
http://arxiv.org/abs/2411.08830
Autor:
d'Elbée, Christian
We continue our study of the Wilson conjecture for $\omega$-categorical Lie algebras and prove that $\omega$-categorical $4$-Engel Lie algebras of characteristic $3$ are nilpotent. We develop a set of tools to adapt in the definable context some clas
Externí odkaz:
http://arxiv.org/abs/2411.00667
Autor:
d'Elbée, Christian
We prove a version of the Wilson conjecture for $\omega$-categorical $3$-Engel Lie algebras over a field of characteristic $5$: every $\omega$-categorical Lie algebra over $\mathbb{F}_5$ which satisfies the identity $[x,y^3] = 0$ is nilpotent. We als
Externí odkaz:
http://arxiv.org/abs/2411.00669
Autor:
Vaughan-Lee, Michael
In my article 5-Engel algebras published on the arXiv in 2023 I proved that 5-Engel Lie algebras of characteristic zero or prime characteristic $p>7$ are nilpotent of class at most 11. In this note I investigate the ideal ID$(x)$ generated by an elem
Externí odkaz:
http://arxiv.org/abs/2410.11524
Graded contractions of certain non-toral $\mathbb{Z}_2^3$-gradings on the simple Lie algebras $\mathfrak{so}(7,\mathbb C)$ and $\f{so}(8,\mathbb C)$ are classified up to two notions of equivalence. In particular, there arise two large families of Lie
Externí odkaz:
http://arxiv.org/abs/2409.18069
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
We study the existence of certain characteristically nilpotent Lie algebras with flat coadjoint orbits. Their connected, simply connected Lie groups admit square-integrable representations modulo the center. There are many examples of nilpotent Lie g
Externí odkaz:
http://arxiv.org/abs/2408.10660
Autor:
Latorre, A., Ugarte, L.
We classify nilpotent Lie algebras with complex structures of weakly non-nilpotent type in real dimension eight, which is the lowest dimension where they arise. Our study, together with previous results on strongly non-nilpotent structures, completes
Externí odkaz:
http://arxiv.org/abs/2407.18692
Autor:
Ouaridi, A. Fernandez, Towers, D. A.
A characterization of the finite-dimensional Leibniz algebras with an abelian subalgebra of codimension two over a field $\mathbb{F}$ of characteristic $p\neq2$ is given. In short, a finite-dimensional Leibniz algebra of dimension $n$ with an abelian
Externí odkaz:
http://arxiv.org/abs/2407.11757