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pro vyhledávání: '"Molina, Mauricio Godoy"'
From the classical theory of Lie algebras, it is well-known that the bilinear form $B(X,Y)={\rm tr}(XY)$ defines a non-degenerate scalar product on the simple Lie algebra ${\mathfrak{sl}}(n,{\mathbb R})$. Diagonalizing the Gram matrix $Gr$ associated
Externí odkaz:
http://arxiv.org/abs/2410.15478
In this paper, we study the mechanical system associated with rolling a Lorentzian manifold $(M,g)$ of dimension $n+1\geq2$ on flat Lorentzian space $\widehat{M}={\mathbb R}^{n,1}$, without slipping or twisting. Using previous results, it is known th
Externí odkaz:
http://arxiv.org/abs/2408.05863
Autor:
Molina, Mauricio Godoy
We give sufficient conditions on a labeled direct graph to determine whether the Tanaka prolongation of its associated Lie algebra is infinite-dimensional. In the case that all directed edges are labeled differently, the corresponding graph Lie algeb
Externí odkaz:
http://arxiv.org/abs/2402.07873
Autor:
Molina, Mauricio Godoy, Lagos, Diego
We present a construction of 2-step nilpotent Lie algebras using labeled directed simple graphs, which allows us to give a criterion to detect certain ideals and subalgebras by finding special subgraphs. We prove that if a label occurs only once, the
Externí odkaz:
http://arxiv.org/abs/2308.00272
Autor:
Molina, Mauricio Godoy, Lagos, Diego
The aim of this paper is to investigate the algebraic structure that appears on $|3|-$gradings $\mathfrak{n}=\mathfrak{n}_{-3}\oplus \cdots \oplus \mathfrak{n}_3$ of a complex simple Lie algebra $\mathfrak{n}$. In particular, we completely determine
Externí odkaz:
http://arxiv.org/abs/2306.02605
Autor:
Molina, Mauricio Godoy, Markina, Irina
We study the interplay between geodesics on two non-holono\-mic systems that are related by the action of a Lie group on them. After some geometric preliminaries, we use the Hamiltonian formalism to write the parametric form of geodesics. We present
Externí odkaz:
http://arxiv.org/abs/2009.00965
Autor:
Furutani, Kenro, Molina, Mauricio Godoy, Markina, Irina, Morimoto, Tohru, Vasil'ev, Alexander
We study possible cases of complex simple graded Lie algebras of depth 2, which are the Tanaka prolongations of pseudo $H$-type Lie algebras arising through representation of Clifford algebras. We show that the complex simple Lie algebras of type $B_
Externí odkaz:
http://arxiv.org/abs/1712.08890
Considering Riemannian submersions, we find necessary and sufficient conditions for when sub-Riemannian normal geodesics project to curves of constant first geodesic curvature or constant first and vanishing second geodesic curvatures. We describe a
Externí odkaz:
http://arxiv.org/abs/1707.05155
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In the present paper we study the rigidity of 2-step Carnot groups, or equivalently, of graded 2-step nilpotent Lie algebras. We prove the alternative that depending on bi-dimensions of the algebra, the Lie algebra structure makes it either always of
Externí odkaz:
http://arxiv.org/abs/1603.00373