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Cohomology of Infinite-Dimensional Lie Algebras

  • D. B. Fuks

Part of the Contemporary Soviet Mathematics book series (MCMA)

Table of contents

  1. Front Matter
    Pages i-xii
  2. D. B. Fuks
    Pages 1-60
  3. D. B. Fuks
    Pages 61-207
  4. D. B. Fuks
    Pages 209-317
  5. Back Matter
    Pages 319-339

About this book

Introduction

There is no question that the cohomology of infinite­ dimensional Lie algebras deserves a brief and separate mono­ graph. This subject is not cover~d by any of the tradition­ al branches of mathematics and is characterized by relative­ ly elementary proofs and varied application. Moreover, the subject matter is widely scattered in various research papers or exists only in verbal form. The theory of infinite-dimensional Lie algebras differs markedly from the theory of finite-dimensional Lie algebras in that the latter possesses powerful classification theo­ rems, which usually allow one to "recognize" any finite­ dimensional Lie algebra (over the field of complex or real numbers), i.e., find it in some list. There are classifica­ tion theorems in the theory of infinite-dimensional Lie al­ gebras as well, but they are encumbered by strong restric­ tions of a technical character. These theorems are useful mainly because they yield a considerable supply of interest­ ing examples. We begin with a list of such examples, and further direct our main efforts to their study.

Keywords

Characteristic class Finite algebra bordism boundary element method character classification cohomology form graph homology lie algebra mathematics real number theorem

Authors and affiliations

  • D. B. Fuks
    • 1
  1. 1.Moscow State UniversityMoscowUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-8765-7
  • Copyright Information Consultants Bureau, New York 1986
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-8767-1
  • Online ISBN 978-1-4684-8765-7
  • Buy this book on publisher's site