Results 81 to 90 of about 1,969,963 (254)
Noncomplete affine structures on Lie algebras of maximal class
International Journal of Mathematics and Mathematical Sciences, 2002 Every affine structure on Lie algebra 𝔤 defines a representation of 𝔤 in aff(ℝn). If 𝔤 is a nilpotent Lie algebra provided with a complete affine structure then the corresponding representation is nilpotent.
E. Remm, Michel Goze
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Lie algebra expansion and integrability in superstring Sigma-models
Journal of High Energy Physics, 2020 Lie algebra expansion is a technique to generate new Lie algebras from a given one. In this paper, we apply the method of Lie algebra expansion to superstring σ-models with a ℤ4 coset target space.
Andrea Fontanella, Luca Romano
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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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Post-Lie Algebras, Factorization Theorems and Isospectral-Flows
, 2017 In these notes we review and further explore the Lie enveloping algebra of a post-Lie algebra. From a Hopf algebra point of view, one of the central results, which will be recalled in detail, is the existence of a second Hopf algebra structure.
B Vallette +24 more
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On a conjecture on transposed Poisson n-Lie algebras
AIMS MathematicsThe notion of a transposed Poisson $ n $-Lie algebra has been developed as a natural generalization of a transposed Poisson algebra. It was conjectured that a transposed Poisson $ n $-Lie algebra with a derivation gives rise to a transposed Poisson $ (n ...
Junyuan Huang +3 more
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An elementary approach to the model structure on DG-Lie algebras [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 2023 This paper contains an elementary proof of the existence of the classical model structure on the category of unbounded DG-Lie algebras over a field of characteristic zero, with an emphasis on the properties of free and semifree extensions, which are ...
Emma Lepri
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Journal of Algebra, 2011 A finite-dimensional Lie algebra $L$ over a field $F$ is called an $A$-algebra if all of its nilpotent subalgebras are abelian. This is analogous to the concept of an $A$-group: a finite group with the property that all of its Sylow subgroups are abelian. These groups were first studied in the 1940s by Philip Hall, and are still studied today.
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Post-Lie algebra structures on pairs of Lie algebras
Journal of Algebra, 2016 We study post-Lie algebra structures on pairs of Lie algebras $(\mathfrak{g},\mathfrak{n})$, motivated by nil-affine actions of Lie groups. We prove existence results for such structures depending on the interplay of the algebraic structures of $\mathfrak{g}$ and $\mathfrak{n}$.
Dietrich Burde, Karel Dekimpe
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Quasiclassical Lie Algebras [PDF]
Journal of Algebra, 2001 AbstractIn this paper we study finite dimensional non-semisimple Lie algebras that can be obtained as Lie algebras of skew-symmetric elements of associative algebras with involution. We call such algebras quasiclassical and characterize them in terms of existence of so-called “∗-plain” representations. We show that the theory of ∗-plain representations
Baranov, AA, Zalesskii, AE
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The Lie Algebra of Smooth Sections of a T-bundle
International Journal of Industrial Engineering and Production Research, 2006 In this article, we generalize the concept of the Lie algebra of vector fields to the set of smooth sections of a T-bundle which is by definition a canonical generalization of the concept of a tangent bundle.
M. Nadjafikhah, H. R. Salimi Moghaddam
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