Displaying similar documents to “CR-structures on a real Lie algebra”

Deformations of CR-structures on a real Lie-algebra

Daniele Gouthier (1999)

Bollettino dell'Unione Matematica Italiana

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Sia g 0 un’algebra di Lie e (p, J) una sua struttura di Cauchy-Riemann, vale a dire J è una struttura complessa integrabile del sottospazio vettoriale p. Come è stato fatto per il caso delle strutture complesse, cfr. [GT], introduciamo il concetto di deformazione di una struttura CR. Per mezzo dei gruppi di coomologia H k ⁢ g , q vengono provati risultati di rigidità. In particolare ogni struttura di Lie- CR che è semisemplice è rigida. Alcuni esempi chiariscono le soluzioni particolari esposte. ...

Algorithmic computations of Lie algebras cohomologies

Šilhan, Josef

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From the text: The aim of this work is to advertise an algorithmic treatment of the computation of the cohomologies of semisimple Lie algebras. The base is Kostant’s result which describes the representation of the proper reductive subalgebra on the cohomologies space. We show how to (algorithmically) compute the highest weights of irreducible components of this representation using the Dynkin diagrams. The software package L i E offers the data structures and corresponding procedures for...

The variety of dual mock-Lie algebras

Luisa M. Camacho, Ivan Kaygorodov, Viktor Lopatkin, Mohamed A. Salim (2020)

Communications in Mathematics

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We classify all complex 7 - and 8 -dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex 9 -dimensional dual mock-Lie algebras.

When unit groups of continuous inverse algebras are regular Lie groups

Helge Glöckner, Karl-Hermann Neeb (2012)

Studia Mathematica

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It is a basic fact in infinite-dimensional Lie theory that the unit group A × of a continuous inverse algebra A is a Lie group. We describe criteria ensuring that the Lie group A × is regular in Milnor’s sense. Notably, A × is regular if A is Mackey-complete and locally m-convex.

Extensions of hom-Lie algebras in terms of cohomology

Abdoreza R. Armakan, Mohammed Reza Farhangdoost (2017)

Czechoslovak Mathematical Journal

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We study (non-abelian) extensions of a given hom-Lie algebra and provide a geometrical interpretation of extensions, in particular, we characterize an extension of a hom-Lie algebra 𝔤 by another hom-Lie algebra 𝔥 and discuss the case where 𝔥 has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, Maurer-Cartan formula, curvature and the Bianchi identity for the possible extensions in differential geometry. Moreover, we find a cohomological...

Universal central extension of direct limits of Hom-Lie algebras

Valiollah Khalili (2019)

Czechoslovak Mathematical Journal

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We prove that the universal central extension of a direct limit of perfect Hom-Lie algebras ( ℒ i , α ℒ i ) is (isomorphic to) the direct limit of universal central extensions of ( ℒ i , α ℒ i ) . As an application we provide the universal central extensions of some multiplicative Hom-Lie algebras. More precisely, we consider a family of multiplicative Hom-Lie algebras { ( sl k ( å ) , α k ) } k ∈ I and describe the universal central extension of its direct limit.

Quantization of semisimple real Lie groups

Kenny De Commer (2024)

Archivum Mathematicum

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We provide a novel construction of quantized universal enveloping * -algebras of real semisimple Lie algebras, based on Letzter’s theory of quantum symmetric pairs. We show that these structures can be ‘integrated’, leading to a quantization of the group C * -algebra of an arbitrary semisimple algebraic real Lie group.