Results 31 to 40 of about 1,211 (118)

Struktur Simplektik pada Aljabar Lie Affine aff(2,R)

Jambura Journal of Mathematics
In this research, we studied the affine Lie algebra aff(2,R). The aim of this research is to determine the 1-form in affine Lie algebra aff(2,R) which is associated with its symplectic structure so that affine Lie algebra aff(2,R) is a Frobenius Lie ...
Aurillya Queency, Edi Kurniadi, Firdaniza Firdaniza   +2 more
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Characterizations of Lie n-Centralizers on Certain Trivial Extension Algebras

Journal of Mathematics, 2023
In this paper, we describe the structure of Lie n-centralizers of a trivial extension algebra. We then present some conditions under which a Lie n-centralizer on a trivial extension algebra is proper.
Xiaokui Li, He Yuan, Qian Zhang
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On derived Lie algebras [PDF]

Archiv der Mathematik
Abstract In this paper, we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the corresponding problem for groups.
Salvatore Siciliano, David A. Towers
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Leibniz Algebras and Lie Algebras [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2013
This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.
Mason, G., Yamskulna, G.
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Batalin-Vilkovisky formality for Chern-Simons theory

Journal of High Energy Physics, 2021
We prove that the differential graded Lie algebra of functionals associated to the Chern-Simons theory of a semisimple Lie algebra is homotopy abelian. For a general field theory, we show that the variational complex in the Batalin-Vilkovisky formalism ...
Ezra Getzler
doaj   +1 more source

Lie Bialgebras on the Rank Two Heisenberg–Virasoro Algebra

Mathematics, 2023
The rank two Heisenberg–Virasoro algebra can be viewed as a generalization of the twisted Heisenberg–Virasoro algebra. Lie bialgebras play an important role in searching for solutions of quantum Yang–Baxter equations.
Yihong Su, Xue Chen
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THE NON-DEGENERACY OF THE SKEW-SYMMETRIC BILINEAR FORM OF THE FINITE DIMENSIONAL REAL FROBENIUS LIE ALGEBRA

Barekeng, 2022
A Frobenius Lie algebra is recognized as the Lie algebra whose stabilizer at a Frobenius functional is trivial. This condition is equivalent to the existence of a skew-symmetric bilinear form which is non-degenerate.
Edi Kurniadi
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On Properties of Five-dimensional Nonstandard Filiform Lie algebra

Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023
In this paper, we study the five-dimensional nonstandard Filiform Lie algebra and their basis elements representations. The aim of this research is to determine the basis elements of five-dimensional nonstandard Filiform Lie algebras representation in ...
Ricardo Eka Putra, Edi Kurniadi, Ema Carnia   +2 more
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Hom-structures on semi-simple Lie algebras

Open Mathematics, 2015
A Hom-structure on a Lie algebra (g,[,]) is a linear map σ W g σ g which satisfies the Hom-Jacobi identity: [σ(x), [y,z]] + [σ(y), [z,x]] + [σ(z),[x,y]] = 0 for all x; y; z ∈ g. A Hom-structure is referred to as multiplicative if it is also a Lie algebra
Xie Wenjuan, Jin Quanqin, Liu Wende
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Solvable Lie A-algebras [PDF]

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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