Abstract
The main topic of this chapter is the presentation of the diffeomorphism invariant full Colombeau algebra Gd(Ω) as it was given in [Gro01], yet with a considerable simplification concerning the definition of the ideal N. After envisaging sheaf-theoretic properties of Gd(Ω) and some applications, we discuss a family of related algebras to highlight the general constraints for constructing diffeomorphism invariant full Colombeau algebras. Let us anticipate at this point that Gd(Ω)—which can be considered as the “local” case—will be the basis for the construction of the intrinsically defined full Colombeau algebras on a general smooth manifold in Section 3.3.
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© 2001 Springer Science+Business Media Dordrecht
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Grosser, M., Kunzinger, M., Oberguggenberger, M., Steinbauer, R. (2001). Diffeomorphism Invariant Colombeau Theory. In: Geometric Theory of Generalized Functions with Applications to General Relativity. Mathematics and Its Applications, vol 537. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9845-3_2
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DOI: https://doi.org/10.1007/978-94-015-9845-3_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5880-5
Online ISBN: 978-94-015-9845-3
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