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175 pages, year of publication: 2011

price: 35.50 €

Classification and Structure Theory of Lie Algebras of Smooth Sections

This dissertation focusses on the structure of Lie algebras of smooth and k-times differentiable sections of finite-dimensional Lie algebra bundles, which are generalizations of the famous and well-understood affine Kac-Moody algebras. Besides answering the immediate structural questions (center, commutator algebra, derivations, centroid, automorphism group), this work approaches a classification of section algebras by homotopy theory. Furthermore, we determine a universal invariant symmetric bilinear form on Lie algebras of smooth sections and use this form to define a natural central extension which is universal, at least in the case of Lie algebra bundles with compact base manifold.

- Lie-Algebra
- Lie-Algebren-Bündel
- Zentrale Erweiterung
- Kac-Moody-Algebra
- Vektorbündel

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