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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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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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A Spectral Sequence for Locally Free Isometric Lie Group Actions
We present a spectral sequence for free isometric Lie algebra actions (and consequently locally free isometric Lie group actions) which relates the...
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A multiphase eigenvalue problem on a stratified Lie group
We consider a multiphase spectral problem on a stratified Lie group. We prove the existence of an eigenfunction of (2, q )-eigenvalue problem on a...
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Isometric Lie 2-Group Actions on Riemannian Groupoids
We study isometric actions of Lie 2-groups on Riemannian groupoids by exhibiting some of their immediate properties and implications. Firstly, we...
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Lie Algebra of the DSER Elementary Orthogonal Group
In this article, we find the subalgebra of the orthogonal Lie algebra corresponding to the DSER elementary orthogonal group on a quadratic space with...
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Expansive Lie Group Actions
In this work, we introduce a concept of expansiveness for actions of connected Lie groups. We study some of its properties and investigate some...
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Left-Invariant Minimal Unit Vector Fields on the Solvable Lie Group
Božek (1980) has introduced a class of solvable Lie groups G n with arbitrary odd dimension to construct irreducible generalized symmetric Riemannian...
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Principal bundles and connections modelled by Lie group bundles
In this work, generalized principal bundles modelled by Lie group bundle actions are investigated. In particular, the definition of equivariant...
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Characterizations of extra-invariant spaces under the left translations on a Lie group
In the context of a connected, simply connected nilpotent Lie group, whose representations are square-integrable modulo the center, we find...
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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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Banach Poisson–Lie Group Structure on \( \operatorname {U}( \mathcal {H})\)
We construct a Banach Poisson–Lie group structure on the unitary group of a separable complex Hilbert space.
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THE STRUCTURE OF AN ABELIAN GROUP WHOSE ENDOMORPHISM RING IS A SOLVABLE LIE RING
This paper finds the structure of an Abelian group with maximal or minimal condition when its endomorphism ring is a solvable Lie ring.
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Reductive Homogeneous Spaces of the Compact Lie Group \(G_2\)
The first author defended her doctoral thesis “Espacios homogéneos reductivos y álgebras no asociativas” in 2001, supervised by P. Benito and A....
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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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The Chain Control Set of Discrete-Time Linear Systems on the Affine Two-Dimensional Lie Group
In this paper, we present conditions for the existence and uniqueness of chain control sets of discrete-time linear systems on the affine...
