Results 31 to 40 of about 107,381 (262)
Noncommutative Differentials on Poisson-Lie groups and pre-Lie algebras [PDF]
, 2014 We show that the quantisation of a connected simply-connected Poisson-Lie group admits a left-covariant noncommutative differential structure at lowest deformation order if and only if the dual of its Lie algebra admits a pre-Lie algebra structure. As an
S. Majid, Wenqing Tao
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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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Growth and form, Lie algebras and special functions
Mathematical Biosciences and Engineering, 2021 The formation of a biological organism, or an organ within it, can often be regarded as the unfolding of successive equilibria of a mechanical system. In a mathematical model, these changes of equilibria may be considered to be responses of mechanically ...
Raghu Raghavan
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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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Deformations of homomorphisms of Lie groups and Lie algebras
, 1967 The purpose of this note is to announce several results on deformations of homomorphisms of Lie groups and Lie algebras. Our main theorems are precise analogues of two basic theorems on deformations of complex analytic structures on compact manifolds ...
A. Nijenhuis, R. Richardson
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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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Clifford algebras and their applications to Lie groups and spinors [PDF]
, 2017 In these lectures, we discuss some well-known facts about Clifford algebras: matrix representations, Cartan's periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in $n$ dimensions, etc ...
Dmitry Shirokov
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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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Quantizations on Nilpotent Lie Groups and Algebras Having Flat Coadjoint Orbits [PDF]
Journal of Geometric Analysis, 2016 For a connected simply connected nilpotent Lie group $$\textsf {G}$$G with Lie algebra $${{\mathfrak {g}}}$$g and unitary dual $$\widehat{{\textsf {G}}}$$G^ one has (a) a global quantization of operator-valued symbols defined on $$\textsf {G}\times ...
M. Măntoiu, Michael Ruzhansky
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