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Geometric and Lie-Theoretic Principles in Pure and Applied Deformation Theory

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Deformation Theory of Algebras and Structures and Applications

Part of the book series: NATO ASI Series ((ASIC,volume 247))

Abstract

These notes develop a geometric point of view in the theory of deformation of structures, emphasizing the role of the orbit space of a group of symmetries of a system of differential equations acting on the space of solutions. The usual infinitesimal deformation space—which appears as a cohomology group in many special situations—is the tangent space to this space of orbits. The classical theory of deformation of complex structures is presented first as a model, then the deformation of the Cartan-Maurer equations is discussed from a differential form point of view, leading in a very natural way to Chevalley-Eilenberg cohomology. Relations with certain aspects of mathematical physics and control theory are also evident.

This work was also partially supported by a grant from the Applied Mathematics Program of the National Science Foundation.

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Authors and Affiliations

  1. National Research Council Senior Research Associate, Ames Research Center of NASA, 94035, Moffett Field, CA, USA

    Robert Hermann

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  1. Robert Hermann
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Editors and Affiliations

  1. CWI, University of Utrecht, Amsterdam, The Netherlands

    Michiel Hazewinkel

  2. University of Pennsylvania, Philadelphia, PA, USA

    Murray Gerstenhaber

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© 1988 Kluwer Academic Publishers

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Hermann, R. (1988). Geometric and Lie-Theoretic Principles in Pure and Applied Deformation Theory. In: Hazewinkel, M., Gerstenhaber, M. (eds) Deformation Theory of Algebras and Structures and Applications. NATO ASI Series, vol 247. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3057-5_13

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  • DOI: https://doi.org/10.1007/978-94-009-3057-5_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7875-7

  • Online ISBN: 978-94-009-3057-5

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