Results 1 to 10 of about 101 (83)
The Principal Element of a Frobenius Lie Algebra [PDF]
Letters in Mathematical Physics, 2009 We introduce the notion of the \textit{principal element} of a Frobenius Lie algebra $\f$. The principal element corresponds to a choice of $F\in \f^*$ such that $F[-,-]$ non-degenerate. In many natural instances, the principal element is shown to be semisimple, and when associated to $\sl_n$, its eigenvalues are integers and are independent of $F ...
Anthony Giaquinto, Murray Gerstenhaber
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Deforming lie algebras to frobenius integrable nonautonomous hamiltonian systems [PDF]
Reports on Mathematical Physics, 2021 Motivated by the theory of Painlevé 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 vector fields can be deformed to a time-dependent Lie algebra of Frobenius integrable vector fields ...
Artur Sergyeyev +2 more
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Levi Decomposition of Frobenius Lie Algebra of Dimension 6
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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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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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.
Evgeny Khukhro
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Frobenius–Schur indicators for semisimple Lie algebras
Journal of Algebra, 2007 12 pages, to appear in Journal of ...
Shlomo Gelaki
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Nilpotency of Lie Type Algebras with Metacyclic Frobenius Groups of Automorphisms
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.
Natalia Makarenko
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Journal of Physics: Conference Series, 2021 Abstract In this present paper, we study real Frobenius Lie algebras constructed from non-commutative nilpotent Lie algebras of dimension ≤ 4. The main purpose is to obtain Frobenius Lie algebras of dimension ≤ 6. Particularly, for a given non-commutative nilpotent Lie algebras N of dimension ≤ 4 we show that there exist commutative ...
E Kurniadi, E Carnia, A K Supriatna
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The Frobenius semiradical of a Lie algebra
Journal of Algebra, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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
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