Displaying similar documents to “Non-abelian extensions of infinite-dimensional Lie groups”

Lie group extensions associated to projective modules of continuous inverse algebras

Karl-Hermann Neeb (2008)

Archivum Mathematicum

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We call a unital locally convex algebra A a continuous inverse algebra if its unit group A × is open and inversion is a continuous map. For any smooth action of a, possibly infinite-dimensional, connected Lie group G on a continuous inverse algebra A by automorphisms and any finitely generated projective right A -module E , we construct a Lie group extension G ^ of G by the group GL A ( E ) of automorphisms of the A -module E . This Lie group extension is a “non-commutative” version of the group Aut ( 𝕍 ) of...

On the cohomology of vector fields on parallelizable manifolds

Yuly Billig, Karl-Hermann Neeb (2008)

Annales de l’institut Fourier

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In the present paper we determine for each parallelizable smooth compact manifold M the second cohomology spaces of the Lie algebra 𝒱 M of smooth vector fields on M with values in the module Ω ¯ M p = Ω M p / d Ω M p - 1 . The case of p = 1 is of particular interest since the gauge algebra of functions on M with values in a finite-dimensional simple Lie algebra has the universal central extension with center Ω ¯ M 1 , generalizing affine Kac-Moody algebras. The second cohomology H 2 ( 𝒱 M , Ω ¯ M 1 ) classifies twists of the semidirect product...

An obstruction to represent abelian Lie algebras by unipotent matrices.

J. C. Benjumea, F. J. Echarte, Núñez, J.,Tenorio, A. F. (2004)

Extracta Mathematicae

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The aim of this paper is the study of abelian Lie algebras as subalgebras of the nilpotent Lie algebra gn associated with Lie groups of upper-triangular square matrices whose main diagonal is formed by 1. We also give an obstruction to obtain the abelian Lie algebra of dimension one unit less than the corresponding to gn as a Lie subalgebra of gn. Moreover, we give a procedure to obtain abelian Lie subalgebras of gn up to the dimension which we think it is the maximum.

Cohomology of Hom-Lie superalgebras and q -deformed Witt superalgebra

Faouzi Ammar, Abdenacer Makhlouf, Nejib Saadaoui (2013)

Czechoslovak Mathematical Journal

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Hom-Lie algebra (superalgebra) structure appeared naturally in q -deformations, based on σ -derivations of Witt and Virasoro algebras (superalgebras). They are a twisted version of Lie algebras (superalgebras), obtained by deforming the Jacobi identity by a homomorphism. In this paper, we discuss the concept of α k -derivation, a representation theory, and provide a cohomology complex of Hom-Lie superalgebras. Moreover, we study central extensions. As application, we compute derivations and...