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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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The Discontinuity Group of a Locally Bounded Homomorphism of a Connected Lie Group into a Connected Lie Group Is Commutative
AbstractWe prove that the discontinuity group of every locally bounded homomorphism of a Lie group into a Lie group is not only compact and...
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Automatic Continuity of every Locally Bunded Homomorphism of a Perfect Connected Lie Group to a Connected Lie Group
AbstractOne of the simplest and most important results following directly from the commutativity of the discontinuity group of a locally bounded...
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Clustering of Image Covariance Matrixes on Lie Group Manifold
AbstractAn image clustering method based on covariance matrix and mean-shift algorithm on Lie group manifold is proposed. Firstly, according to the...
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Evaluation and implementation of Lie group integration methods for rigid multibody systems
As commonly known, standard time integration of the kinematic equations of rigid bodies modeled with three rotation parameters is infeasible due to...
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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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Lie group analysis of the general Karmarkar condition
The Karmarkar embedding condition in different spherically symmetrical metrics is studied in general using Lie symmetries. In this study, the Lie...
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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 Group Generalizations of Coherent States
This chapter forms the core of this book. The first half of this chapter discusses in detail the general group-theoretical procedure for constructing...
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Extension of Characters from the Radical of a Connected Lie Group to a One-Dimensional Pure Pseudorepresentation of the Group Revisited
AbstractInvestigations concerning the extension of characters on normal subgroups to one-dimensional pure pseudorepresentations of the envelo**...
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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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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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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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