Results 11 to 20 of about 27,580 (162)
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 ...
Gerstenhaber, Murray, Giaquinto, Anthony
exaly +7 more sources
Quasi-Frobenius-Lusztig kernels for simple Lie algebras [PDF]
Transactions of the American Mathematical Society, 2016 In the first author’s Math. Res. Lett. paper (2014), the quasi-Frobenius-Lusztig kernel associated with s l 2 \mathfrak {sl}_{2} was constructed. In this paper we construct the quasi-Frobenius-Lusztig kernels associated with any simple Lie algebra g ...
Liu, Gongxiang +2 more
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Frobenius–Schur indicators for semisimple Lie algebras [PDF]
Journal of Algebra, 2007 12 pages, to appear in Journal of ...
Abu-Hamed, Mohammad, Gelaki, Shlomo
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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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Families of Frobenius seaweed Lie algebras [PDF]
, 2012 We extend the set of known infinite families of Frobenius seaweed Lie subalgebras of $\mathfrak{sl}_{n}$ to include a family which is the first non-trivial general family containing algebras whose associated meanders have an arbitrarily large number of parts.
Coll, Vincent +2 more
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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. Y. Makarenko, Evgeny Khukhro
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Symplectic Double Extensions for Restricted Quasi-Frobenius Lie (Super)Algebras [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2023 In this paper, we present a method of symplectic double extensions for restricted quasi-Frobenius Lie superalgebras. Certain cocycles in the restricted cohomology represent obstructions to symplectic double extension, which we fully describe. We found a necessary condition for which a restricted quasi-Frobenius Lie superalgebras is a symplectic double ...
Bouarroudj, Sofiane +2 more
+7 more sources
The evolution of the spectrum of a Frobenius Lie algebra under deformation [PDF]
Communications in Algebra, 2021 The category of Frobenius Lie algebras is stable under deformation, and here we examine explicit infinitesimal deformations of four and six dimensional Frobenius Lie algebras with the goal of understanding if the spectrum of a Frobenius Lie algebra can evolve under deformation. It can.
Coll, Jr., Vincent E. +2 more
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Flat Lie groups, Frobenius Lie algebras and ��tale prehomogeneous vector spaces for reductive Lie groups [PDF]
, 2018 In this paper, we established the relationship among left-invariant flat connections on Lie groups, left-symmetric algebras, Frobenius Lie algebras and tale prehomogeneous vector spaces, gave a one-to-one correspondence between the left-symmetric Lie algebras with a right identity and the tale prehomogeneous vector spaces for a Lie group, and ...
Yang, Xiaomei, Zhu, Fuhai
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On the classification of 2-solvable Frobenius Lie algebras [PDF]
, 2022 We discuss the classification of 2-solvable Frobenius Lie algebras. We prove that every 2-solvable Frobenius Lie algebra splits as a semidirect sum of an n-dimensional vector space V and an n-dimensional maximal Abelian subalgebra (MASA) of the full space of endomorphisms of V.
Diatta, André +2 more
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