Results 11 to 20 of about 27,512 (159)
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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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.
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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
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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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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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Higher Deformations of Lie Algebra Representations I [PDF]
, 2020 In the late 1980s, Friedlander and Parshall studied the representations of a family of algebras which were obtained as deformations of the distribution algebra of the first Frobenius kernel of an algebraic group.
Westaway, Matthew
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Frobenius–Schur indicators for semisimple Lie algebras
Journal of Algebra, 2007 12 pages, to appear in Journal of ...
Abu-Hamed, Mohammad, Gelaki, Shlomo
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Symplectic Double Extensions for Restricted Quasi-Frobenius Lie (Super)Algebras
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
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Geometric construction of D-branes in WZW models [PDF]
, 2011 The geometric description of D-branes in WZW models is pushed forward. Our starting point is a gluing condition\, $J_{+}=FJ_-$ that matches the model's chiral currents at the worldsheet boundary through a linear map $F$ acting on the WZW Lie algebra. The
AY Alekseev +38 more
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