Results 21 to 30 of about 667 (261)
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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Lie groups and Lie algebras [PDF]
, 2012 We have studied linear transformation on \({\mathbb{R}}^{n}\) using the traditional matrix formalism in Chap. 7 and more generally in Chaps. 8–10, using the machinery of geometric algebra. This chapter explains the bivector interpretation of a general linear operator and offers a new proof of the Cayley–Hamilton theorem based upon this interpretation.
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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 \(\operatorname {ad}{\mathfrak g}\).
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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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The Recursive Forward Dynamics of Flexible Mechanical Systems
MATEC Web of Conferences, 2016 Lie groups and Lie algebras are used to study the recursive dynamics of flexible multi-body systems. First the adjoint transformations and adjoint operators of Lie groups and Lie algebras are discussed.
Shao Bing, Yuan Entao
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Generalisation of affine Lie algebras on compact real manifolds
SciPost Physics Proceedings, 2023 We report on recent work concerning a new type of generalised Kac-Moody algebras based on the spaces of differentiable mappings from compact manifolds or homogeneous spaces onto compact Lie groups.
Rutwig Campoamor-Stursberg, Marc de Montigny, Michel Rausch de Traubenberg
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Overview remarks on homogeneous, N = 1, d = 11 supergravity cosmologies [PDF]
, 1988 The dynamics of the full class of homogeneous N = 1, d = 11 supergravity world models is investigated. By using the classification of Lie algebras of Lie groups which act simply transitively on 6- and 7-dimensional compact spaces some conclusions are ...
Szczęsny, J. +2 more
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