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Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras
This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the...
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Lie Group and Lie Derivative
This chapter begins with a brief review of Lie groups and their Lie algebras. Subsequently, it introduces the notion of the Lie derivative, its...
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Super-biderivations and Post-Lie Superalgebras on Some Lie Superalgebras
In this paper, all symmetric super-biderivations of some Lie superalgebras are determined. As an application, commutative post-Lie superalgebra...
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Lie Bialgebra Structure of Derivation Lie Algebra over Quantum Torus
In this paper, all Lie bialgebra structures on the derivation Lie algebra W over a rank d ≥ 3 quantum torus associated to q are considered, where q ...
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Sophus Lie
Sophus Lie nait en 1842 à Nordfjordeide (Norvège) dans une famille de petite bourgeoisie (son père est pasteur). Après ses études secondaires, il...
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Hom-Lie Algebras with Derivations
In this paper, we first introduce the notion of an HLieDer triple, which includes a Hom-Lie algebra and a derivation. We define a cohomology theory...
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Lie Group
A Lie group is a group (in algebraic sense), which is also a differentiable manifold, with the property that the group operations are compatible with...
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Casimir preserving stochastic Lie–Poisson integrators
Casimir preserving integrators for stochastic Lie–Poisson equations with Stratonovich noise are developed, extending Runge–Kutta Munthe-Kaas methods....
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Lie hyperalgebras
We define the Lie hyperalgebra of a Lie hypergroup as the smallest (possibly infinite dimensional) Lie algebra containing left invariant vector...
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Biderivations of Hom-Lie Algebras and Superalgebras
On Hom-Lie algebras and superalgebras, we introduce the notions of biderivations and linear commuting maps, and compute them for some typical Hom-Lie...
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3-Bihom-ρ-Lie Algebras, 3-Pre-Bihom-ρ-Lie Algebras
The purpose is to introduce the notions of 3-Bihom- ρ -Lie algebras and 3-pre-Bihom- ρ -Lie algebras. The authors describe their constructions and...
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Finite Dimensional Lie Algebras
Another fertile field to explore the link between algebraic relations of the matrices and the properties of their characteristic polynomial is where...
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Finite Dimensional Modules over Indefinite Kac–Moody Lie Algebras
In this paper, we study the finite dimensional modules over indefinite Kac–Moody Lie algebras. We prove that any Kac–Moody Lie algebra with...
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Character Sheaves for Classical Graded Lie Algebras
In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg’s type II...
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Wild Local Structures of Automorphic Lie Algebras
We study automorphic Lie algebras using a family of evaluation maps parametrised by the representations of the associative algebra of functions. This...
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Classifications of Dupin hypersurfaces in Lie sphere geometry
This is a survey of local and global classification results concerning Dupin hypersurfaces in S n (or R n ) that have been obtained in the context of...