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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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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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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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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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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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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 Galois action on the lower central series of the fundamental group of the Fermat curve
Information about the absolute Galois group G K of a number field K is encoded in how it acts on the étale fundamental group π of a curve X defined...
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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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The Dixmier–Douady class, the action homomorphism, and group cocycles on the symplectomorphism group
Let X be a one-connected and integral symplectic manifold. In this paper, we construct and study a two-cocycle and three-cocycle on the...
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Differential equations and Lie group representations
We discuss the role of differential equations in Lie group representation theory. We use Kashiwara’s pentagon as a reference frame for the real...
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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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Topological and Homological Properties of the Orbit Space of a Simple Three-Dimensional Compact Linear Lie Group
AbstractThe question of whether an orbit space of a compact linear group is a topological manifold and a homology manifold is studied. The case of...
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Geometry-Preserving Numerical Methods for Physical Systems with Finite-Dimensional Lie Algebras
We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on...
