Results 1 to 10 of about 27,580 (162)
Deforming Lie algebras to Frobenius integrable non-autonomous Hamiltonian systems [PDF]
Reports on Mathematical Physics, 2020 Motivated by the theory of Painlev\'e equations and associated hierarchies, we study non-autonomous Hamiltonian systems that are Frobenius integrable. We establish sufficient conditions under which a given finite-dimensional Lie algebra of Hamiltonian ...
Blaszak, Maciej +2 more
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Levi Decomposition of Frobenius Lie Algebra of Dimension 6 [PDF]
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2022 In this paper, we study notion of the Lie algebra of dimension 6. The finite dimensional Lie algebra can be expressed in terms of decomposition between Levi subalgebra and the maximal solvable ideal.
Henti Henti, Edi Kurniadi, Ema Carnia
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Meander graphs and Frobenius Seaweed Lie algebras [PDF]
Journal of Generalized Lie Theory and Applications, 2011 The index of a seaweed Lie algebra can be computed from its associated meander graph. We examine this graph in several ways with a goal of determining families of Frobenius (index zero) seaweed algebras.
Dergachev +6 more
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A Left-Symmetric Structure on The Semi-Direct Sum Real Frobenius Lie Algebra of Dimension 8 [PDF]
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2022 Let be the Lie algebra of the semi-direct sum of the real vector space and the Lie algebra of the sets of all real matrices. In this paper, a Frobenius functional is constructed in order for the Lie algebra to be the real Frobenius Lie algebra of ...
Edi Kurniadi +2 more
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Quasi-Associative Algebras on the Frobenius Lie Algebra M_3 (R)⊕gl_3 (R)
Al-Jabar, 2021 In this paper, we study the quasi-associative algebra property for the real Frobenius Lie algebra of dimension 18. The work aims to prove that is a quasi-associative algebra and to compute its formulas explicitly.
Henti Henti, Edi Kurniadi, Ema Carnia
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On properties of principal elements of Frobenius Lie algebras [PDF]
, 2014 We investigate the properties of principal elements of Frobenius Lie algebras, following the work of M. Gerstenhaber and A. Giaquinto. We prove that any Lie algebra with a left symmetric algebra structure can be embedded, in a natural way, as a ...
Diatta, Andre, Manga, Bakary
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$\mathfrak{g}$-quasi-Frobenius Lie algebras [PDF]
Archivum Mathematicum, 2016 Summary: A Lie version of Turaev's \(\overline{G}\)-Frobenius algebras from \(2\)-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a \(\mathfrak{g}\)-\textit{quasi-Frobenius Lie algebra} for \(\mathfrak{g}\) a finite dimensional Lie algebra.
David N. Pham
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Lie algebras with Frobenius dihedral groups of automorphisms [PDF]
Journal of Algebra, 2023 Suppose that a Lie algebra $L$ admits a finite Frobenius group of automorphisms $FH$ with cyclic kernel $F$ and complement $H$ of order 2, such that the fixed-point subalgebra of $F$ is trivial and the fixed-point subalgebra of $H$ is metabelian. Then the derived length of $L$ is bounded by a constant.
N. Yu. Makarenko
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Barekeng, 2022 A Frobenius Lie algebra is recognized as the Lie algebra whose stabilizer at a Frobenius functional is trivial. This condition is equivalent to the existence of a skew-symmetric bilinear form which is non-degenerate.
Edi Kurniadi
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Nilpotency of Lie Type Algebras with Metacyclic Frobenius Groups of Automorphisms [PDF]
Siberian Mathematical Journal, 2023 Suppose that a Lie type algebra L over a field K admits a Frobenius group of automorphisms FH with cyclic kernel F of order n and complement H such that the fixed-point subalgebra of F is trivial and the fixed-point subalgebra of H is nilpotent of class c.
N. Yu. Makarenko
+7 more sources