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Lie algebras admitting a metacyclic frobenius group of automorphisms [PDF]
Siberian Mathematical Journal, 2013 19 pages, to appear in Siberian Mathematical Journal, Vol.54 (2013), No. 1.
N Yu Makarenko, E I Khukhro
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Contact and Frobenius solvable Lie algebras with abelian nilradical
Communications in Algebra, 2018The aim of this work is to characterize the families of Frobenius (respectively, contact) solvable Lie algebras that satisfies the following condition: 𝔤 = 𝔥⋉V, where 𝔥⊂𝔤𝔩(V), |dim V−dim 𝔤|≤1 and N...
Maria Alejandra Alvarez, G Salgado
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Classification of Frobenius Lie algebras of dimension $\leq 6$
Publicationes Mathematicae Debrecen, 2007A Lie algebra \(\mathfrak{g}\) is called a Frobenius Lie algebra provided that there is a linear form \(l\in \mathfrak{g}^*\) whose stabilizer with respect to the coadjoint representation of \(\mathfrak{g}\) is trivial. Frobenius Lie algebras are always even dimensional.
Csikós, Balázs, Verhóczki, László
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Computing invariants and semi-invariants by means of Frobenius Lie algebras
Journal of Algebra, 2009 Let U(L) be the enveloping algebra of a finite dimensional Lie algebra L over a field k of characteristic zero, Z(U(L)) its center and Sz(U(L)) its semicenter. A sufficient condition is given in order for Sz(U(L)) to be a polynomial algebra over k. Surprisingly, this condition holds for many Lie algebras, especially among those for which the radical is
Alfons I Ooms
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Principal derivations and codimension one ideals in contact and Frobenius Lie algebras
Communications in Algebra, 2019The aim of this work is twofold. First, we give an inductive procedure to construct a Frobenius (resp. contact) Lie algebra from a contact (resp. Frobenius) Lie algebra.
E Roque, G Salgado
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2018
In this paper, we established the relationship among left-invariant flat connections on Lie groups, left-symmetric algebras, Frobenius Lie algebras and étale prehomogeneous vector spaces, gave a one-to-one correspondence between the left-symmetric Lie algebras with a right identity and the étale prehomogeneous vector spaces for a Lie group, and proved ...
Yang, Xiaomei, Zhu, Fuhai
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In this paper, we established the relationship among left-invariant flat connections on Lie groups, left-symmetric algebras, Frobenius Lie algebras and étale prehomogeneous vector spaces, gave a one-to-one correspondence between the left-symmetric Lie algebras with a right identity and the étale prehomogeneous vector spaces for a Lie group, and proved ...
Yang, Xiaomei, Zhu, Fuhai
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Harmonic Analysis for 4-Dimensional Real Frobenius Lie Algebras
2019A real Frobenius Lie algebra is characterized as the Lie algebra of a real Lie group admitting open coadjoint orbits. In this paper, we study irreducible unitary representations corresponding to open coadjoint orbits for each of 4-dimensional Frobenius Lie algebras.
Edi Kurniadi, Hideyuki Ishi
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1990
A necessary condition to be satisfied by n−1 vector fields in ℝ n in order to have a common first integral is supplied by the compatibility condition of Frobenius integrability theorem. This condition is also generically sufficient for the local existence of such a common first integral.
Jean Moulin Ollagnier +1 more
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A necessary condition to be satisfied by n−1 vector fields in ℝ n in order to have a common first integral is supplied by the compatibility condition of Frobenius integrability theorem. This condition is also generically sufficient for the local existence of such a common first integral.
Jean Moulin Ollagnier +1 more
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Deforming lie algebras to frobenius integrable nonautonomous hamiltonian systems
Reports on Mathematical Physics, 2021Maciej Błaszak +2 more
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