Results 11 to 20 of about 102 (87)
On Symmetry Properties of Frobenius Manifolds and Related Lie-Algebraic Structures [PDF]
Symmetry, 2021 The aim of this paper is to develop an algebraically feasible approach to solutions of the oriented associativity equations. Our approach was based on a modification of the Adler–Kostant–Symes integrability scheme and applied to the co-adjoint orbits of the diffeomorphism loop group of the circle.
Anatolij K. Prykarpatski +1 more
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On the Classification of 2-Solvable Frobenius Lie Algebras
Journal of Lie Theory, 2023 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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$\mathfrak{g}$-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.
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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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On the cohomology of frobeniusian model Lie algebras [PDF]
Forum Mathematicum, 2004 We compute the first and second cohomology groups with coefficients in the adjoint module of frobeniusian model algebras whose parameters move in a dense open subset of $\mathbb{C}^{p-1}$, and obtain upper bounds for the dimension of cohomology groups of frobeniusian Lie algebras. Moreover, it is shown that for a dense open subset of $\mathbb{C}^{p-1}$
Ancochea Bermúdez, José María +1 more
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On Properties of Principal Elements of Frobenius Lie Algebras
Journal of Lie Theory, 2014 Latex, 16 pages. The last version appeared at Journal of Lie Theory. Keywords and phrases: Frobenius Lie algebra, affine Lie algebra, Left symmetric Lie algebra, affine motion, symplectic Lie algebra, seaweed Lie algebra, symplectic Lie group, invariant symplectic structure, invariant affine ...
Diatta, André, Manga, Bakary
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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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Meanders and Frobenius Seaweed Lie Algebras
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. Our analysis gives two new families of Frobenius seaweed algebras as well as elementary proofs of known families of such Lie algebras.
Coll, Vincent +2 more
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Quasi-Frobenius-Lusztig kernels for simple Lie algebras
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
Liu, Gongxiang +2 more
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On groups and Lie algebras admitting a Frobenius group of automorphisms
Journal of Pure and Applied Algebra, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Caldeira, Jhone +2 more
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