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Deformation Theory of Algebras and Structures and Applications

  • Michiel Hazewinkel
  • Murray Gerstenhaber

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

Table of contents

  1. Front Matter
    Pages i-viii
  2. The philosophy of deformations: introductory remarks and a guide to this volume

  3. Deformations of algebras

    1. Front Matter
      Pages 9-9
    2. Murray Gerstenhaber, Samuel D. Schack
      Pages 11-264
    3. Michel Goze
      Pages 265-355
    4. C. Roger
      Pages 357-374
    5. José María, Ancochea Bermudez
      Pages 403-445
    6. Murray Gerstenhaber, Samuel D. Schack
      Pages 447-498
  4. Perturbations of algebras in functional analysis and operator theory

    1. Front Matter
      Pages 499-499
    2. Erik Christensen
      Pages 537-556
    3. K. Jarosz
      Pages 557-563
  5. Deformations and moduli in geometry and differential equations and algebras

  6. Deformations of algebras and mathematical and quantum physics

  7. Deformations elsewhere

    1. Front Matter
      Pages 973-973
    2. Francesco Calogero
      Pages 975-980
  8. Back Matter
    Pages 1015-1030

About this book

Introduction

This volume is a result of a meeting which took place in June 1986 at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school. In return it contains a good many results which were not yet available at the time of the meeting. In particular it is now abundantly clear that the Deformation theory of algebras is indeed central to the whole philosophy of deformations/perturbations/stability. This is one of the main results of the 254 page paper below (practically a book in itself) by Gerstenhaber and Shack entitled "Algebraic cohomology and defor­ mation theory". Two of the main philosphical-methodological pillars on which deformation theory rests are the fol­ lowing • (Pure) To study a highly complicated object, it is fruitful to study the ways in which it can arise as a limit of a family of simpler objects: "the unraveling of complicated structures" . • (Applied) If a mathematical model is to be applied to the real world there will usually be such things as coefficients which are imperfectly known. Thus it is important to know how the behaviour of a model changes as it is perturbed (deformed).

Keywords

Algebra Derivation Invariant Manifold Morphism Volume calculus equation function geometry mathematical physics

Editors and affiliations

  • Michiel Hazewinkel
    • 1
  • Murray Gerstenhaber
    • 2
  1. 1.CWIUniversity of UtrechtAmsterdamThe Netherlands
  2. 2.University of PennsylvaniaPhiladelphiaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-3057-5
  • Copyright Information Springer Science+Business Media B.V. 1988
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-7875-7
  • Online ISBN 978-94-009-3057-5
  • Series Print ISSN 1389-2185
  • Buy this book on publisher's site
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