Results 21 to 30 of about 85,352 (227)
Automorphisms of real Lie algebras of dimension five or less [PDF]
, 2013 The Lie algebra version of the Krull-Schmidt Theorem is formulated and proved. This leads to a method for constructing the automorphisms of a direct sum of Lie algebras from the automorphisms of its indecomposable components.
Fisher, David J. +2 more
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Chinese Journal of Mechanical Engineering, 2021 Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms, and the generalized analysis method and concise kinematics transfer matrix are obtained.
Peng Sun +5 more
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Methods of group theory in Leibniz algebras: some compelling results
Researches in Mathematics, 2021 The theory of Leibniz algebras has been developing quite intensively. Most of the results on the structural features of Leibniz algebras were obtained for finite-dimensional algebras and many of them over fields of characteristic zero.
I.Ya. Subbotin
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A new model of the free monogenic digroup
Математичні Студії, 2023 It is well-known that one of open problems in the theory of Leibniz algebras is to find a suitable generalization of Lie’s third theorem which associates a (local) Lie group to any Lie algebra, real or complex. It turns out, this is related to finding an
Yu. V. Zhuchok, G. F. Pilz
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Split abelian chief factors and first degree cohomology for Lie algebras [PDF]
, 2013 In this paper we investigate the relation between the multiplicities of split abelian chief factors of finite-dimensional Lie algebras and first degree cohomology.
Feldvoss, Jörg +2 more
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Lie Groups and Lie Algebras [PDF]
, 2000 A Lie group is a group G that at the same time is a finite-dimensional manifold of differentiability class C2, in such a way that the two group operations of G: $$ \mu :\;\left( {x,y} \right) \mapsto xy:\;G \times G \to G\quad \left( {multiplication} \right)$$ (1.1.1) $$\iota :\;x \mapsto {x^{ - 1}}\quad :G \to G\quad \left( {inversion ...
J. J. Duistermaat, J. A. C. Kolk
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Cohomology and Crossed Modules of Modified Rota–Baxter Pre-Lie Algebras
MathematicsThe goal of the present paper is to provide a cohomology theory and crossed modules of modified Rota–Baxter pre-Lie algebras. We introduce the notion of a modified Rota–Baxter pre-Lie algebra and its bimodule.
Fuyang Zhu, Wen Teng
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A Cornucopia of Carnot Groups in Low Dimensions
Analysis and Geometry in Metric Spaces, 2022 Stratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating.
Le Donne Enrico, Tripaldi Francesca
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Splittable Lie Groups and Lie Algebras
Journal of Algebra, 2000 Let us call a finite-dimensional Lie algebra \(\mathfrak g\) over a field of characteristic zero Malcev splittable if \(\operatorname {ad}{\mathfrak g}\) is splittable in the sense that for each element of \(\operatorname {ad}{\mathfrak g}\) the semisimple and nilpotent Jordan component belong to \(\operatorname {ad}{\mathfrak g}\).
openaire +2 more sources
Algebras of Complete Hörmander Vector Fields, and Lie-Group Construction
Bruno Pini Mathematical Analysis Seminar, 2014 The aim of this note is to characterize the Lie algebras g of the analytic vector fields in RN which coincide with the Lie algebras of the (analytic) Lie groups defined on RN (with its usual differentiable structure). We show that such a characterization
Andrea Bonfiglioli
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