Results 11 to 20 of about 27,600 (150)

On properties of principal elements of Frobenius Lie algebras [PDF]

Journal of Lie Theory, 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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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, Marciniak, Krzysztof, Sergyeyev, Artur   +2 more
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Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields [PDF]

, 1997
We construct a generalization of the variations of Hodge structures on Calabi-Yau manifolds. It gives a Mirror partner for the theory of genus=0 Gromov-Witten invariantsComment: 12 pages, AMS-TeX; typos and a sign corrected, appendix added.
Formality Of Lie Algebras, Frobenius Manifolds, Maxim Kontsevich, Maxim Kontsevich, Maxim Kontsevich, Polyvector Fields, Sergey Barannikov, Sergey Barannikov, Sergey Barannikov   +8 more
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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, Alexander A. Balinsky   +1 more
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Bayesian perspective for orientation determination in cryo-EM with application to structural heterogeneity analysis. [PDF]

Acta Crystallogr D Struct Biol
A Bayesian perspective on orientation estimation in cryo‐EM is presented, with the minimum mean‐square error estimator outperforming standard cross‐correlation‐based approaches, particularly under challenging low signal‐to‐noise conditions. We demonstrate that improved orientation estimation has a decisive impact on 3D reconstruction quality and ...
Xu S, Balanov A, Singer A, Bendory T.
europepmc   +2 more sources

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, Manga, Bakary, Mbaye, Ameth   +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., Mayers, Nicholas, Russoniello, Nicholas   +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, Campoamor-Stursberg, Rutwig   +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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