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Branching Rules for Splint Root Systems
A root system is splint if it is a decomposition into a union of two disjoint root systems. Examples of such root systems arise naturally in studying...
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Minimal representations of Lie algebras with non-trivial Levi decomposition
We obtain minimal dimension matrix representations for each of the Lie algebras of dimensions five, six, seven and eight obtained by Turkowski that...
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Curvature properties of \(\varvec{4}\)-dimensional Riemannian manifolds with a circulant structure
We consider a 4-dimensional Riemannian manifold M equipped with a circulant structure q , which is an isometry with respect to the metric g and
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A New Way to Compute the Rodrigues Coefficients of Functions of the Lie Groups of Matrices
In Theorem 1 we present, in the case when the eigenvalues of the matrix are pairwise distinct, a direct way to determine the general Rodrigues...
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Pre-Lie Groups in Abstract Differential Geometry
We study groups with “differential structure” in the framework of Abstract Differential Geometry, an abstraction of the classical differential...
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Symmetry reduction and exact solutions of a hyperbolic Monge-Ampère equation
By means of the classical symmetry method, a hyperbolic Monge-Ampère equation is investigated. The symmetry group is studied and its corresponding...
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Canonical connection on a class of Reimannian almost product manifolds
The canonical connection on a Reimannian almost product manifold is an analogue to the Hermitian connection on an almost Hermitian manifold. In this...
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Five-dimensional K-contact Lie algebras
We introduce a general approach to the study of left-invariant K -contact structures on Lie groups and we obtain a full classification in dimension...
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Algebraic prolongation and rigidity of Carnot groups
We discuss the known results on rigidity of Carnot groups using Tanaka’s prolongation theory. We also apply Tanaka’s theory to study rigidity of an...
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Do Uncertainty Minimizers Attain Minimal Uncertainty?
The uncertainty principle is a fundamental concept in quantum mechanics, harmonic analysis and signal and information theory. It is rooted in the...
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New HKT manifolds arising from quaternionic representations
We give a procedure for constructing an 8 n -dimensional HKT Lie algebra starting from a 4 n -dimensional one by using a quaternionic representation of...
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The partial positivity of the curvature in Riemannian symmetric spaces
In this paper, the partial positivity (resp., negativity) of the curvature of all irreducible Riemannian symmetric spaces is determined. From the...
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Foliations invariant under Lie group transverse actions
In this paper we study (smooth and holomorphic) foliations which are invariant under transverse actions of Lie groups.
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Tanaka prolongation of free Lie algebras
With the exception of the three step real free Lie algebra on two generators, all real free Lie algebras of step at least three are shown to have...
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A sufficient condition for nonrigidity of Carnot groups
In this article we consider contact map**s on Carnot groups. Namely, we are interested in those map**s whose differential preserves the...
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Reduction by stages and the Raïs-type formula for the index of a Lie algebra with an ideal
For a quite general class of Lie algebras with a nontrivial ideal we derive a formula for the index generalizing the Raïs formula for the index of...
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On the Hopf Algebraic Structure of Lie Group Integrators
A commutative but not cocommutative graded Hopf algebra H N , based on ordered (planar) rooted trees, is studied. This Hopf algebra is a generalization...
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Curvature Estimates for Irreducible Symmetric Spaces
By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, and thus...