Displaying similar documents to “Lie group extensions associated to projective modules of continuous inverse algebras”

Non-abelian extensions of infinite-dimensional Lie groups

Karl-Hermann Neeb (2007)

Annales de l’institut Fourier

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In this article we study non-abelian extensions of a Lie group G modeled on a locally convex space by a Lie group N . The equivalence classes of such extension are grouped into those corresponding to a class of so-called smooth outer actions S of G on N . If S is given, we show that the corresponding set Ext ( G , N ) S of extension classes is a principal homogeneous space of the locally smooth cohomology group H s s 2 ( G , Z ( N ) ) S . To each S a locally smooth obstruction class χ ( S ) in a suitably defined cohomology group...

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...

Algebroid nature of the characteristic classes of flat bundles

Jan Kubarski (1998)

Banach Center Publications

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The following two homotopic notions are important in many domains of differential geometry: - homotopic homomorphisms between principal bundles (and between other objects), - homotopic subbundles. They play a role, for example, in many fundamental problems of characteristic classes. It turns out that both these notions can be - in a natural way - expressed in the language of Lie algebroids. Moreover, the characteristic homomorphisms of principal bundles (the Chern-Weil homomorphism [K4],...

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...