The adjoint representation inside the exterior algebra of a simple Lie algebra [PDF]
Advances in Mathematics, 2015 Final version. More misprints corrected.
Claudio Procesi
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The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2010 The Hamiltonian representation for the hierarchy of Lax-type flows on a dual space to the Lie algebra of shift operators coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is found by means of a ...
Oksana Ye. Hentosh
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Homology of the Lie algebra of vector fields on the line with coefficients in symmetric powers of its adjoint representation [PDF]
Functional Analysis and Its Applications, 2006 We compute the homology of the Lie algebra~$W_1$ of (polynomial)vector fields on a line with coefficients in symmetric powersof its adjoint representation. We also list the results obtained so farfor the homology with coefficients in tensor powers and, in turn, use themfor partially computing the homology of the Liealgebra of currents on a line with ...
Vladimir V Dotsenko
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Useful relations among the generators in the defining and adjoint representations of SU(N)
SciPost Physics Lecture Notes, 2021 There are numerous relations among the generators in the defining and adjoint representations of SU(N). These include Casimir operators, formulae for traces of products of generators, etc.
Howard E. Haber
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Deformations of the three-dimensional Lie algebra sl(2)
Қарағанды университетінің хабаршысы. Математика сериясы, 2020 Deformation is one of key questions of the structural theory of algebras over a field. Especially, it plays a important role in the classification of such algebras.
A.A. Ibrayeva +2 more
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Results in Physics, 2023 Introduction:: The chemical oscillators are identified as open system that demonstrate periodic changes in the concentration of some reaction species as a result of intricate physico-chemical mechanisms which can lead to bi-stability, the occurrence of ...
Ebrahem A. Algehyne +4 more
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Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation [PDF]
, 2020 In this paper, we introduce the notion of a (regular) Hom-Lie group. We associate a Hom-Lie algebra to a Hom-Lie group and show that every regular Hom-Lie algebra is integrable.
Jiang, Jun +2 more
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On special covariants in the exterior algebra of a simple Lie algebra [PDF]
, 2014 We study the subspace of the exterior algebra of a simple complex Lie algebra linearly spanned by the copies of the little adjoint representation or, in the case of the Lie algebra of traceless matrices, by the copies of the n-th symmetric power of the ...
De Concini, Corrado +3 more
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Categorifying the sl(2, C) Knizhnik-Zamolodchikov connection via an infinitesimal 2-Yang-Baxter operator in the string Lie-2-algebra [PDF]
, 2017 We construct a flat (and fake-flat) 2-connection in the configuration space of n indistinguishable particles in the complex plane, which categorifies the sl(2,C)-Knizhnik-Zamolodchikov connection obtained from the adjoint representation of sl(2,C).
Cirio, LS, Martins, JF
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Multiplicity of the Adjoint Representation in Simple Quotients of the Enveloping Algebra of a Simple Lie Algebra [PDF]
Transactions of the American Mathematical Society, 1989 Let g \mathfrak {g} be a complex simple Lie algebra, h \mathfrak {h} a Cartan subalgebra and U ( g ) U(\mathfrak {g}) the enveloping algebra of g \mathfrak {g} . We calculate for each maximal two-sided
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