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Lie Groups and Lie Algebras

Their Representations, Generalisations and Applications

  • B. P. Komrakov
  • I. S. Krasil’shchik
  • G. L. Litvinov
  • A. B. Sossinsky

Part of the Mathematics and Its Applications book series (MAIA, volume 433)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Quantum Mathematics

  3. Hypergroups

    1. Front Matter
      Pages 85-85
    2. V. M. Buchstaber, E. G. Rees
      Pages 85-107
    3. William C. Connett, Alan L. Schwartz
      Pages 109-115
    4. Marc-Olivier Gebuhrer
      Pages 117-131
    5. M. M. Nessibi, M. Sifi
      Pages 133-145
  4. Homogenious Spaces And Lie Algebras and Superalgebras

  5. Representations

  6. Differential Equations

About this book

Introduction

This collection contains papers conceptually related to the classical ideas of Sophus Lie (i.e., to Lie groups and Lie algebras). Obviously, it is impos­ sible to embrace all such topics in a book of reasonable size. The contents of this one reflect the scientific interests of those authors whose activities, to some extent at least, are associated with the International Sophus Lie Center. We have divided the book into five parts in accordance with the basic topics of the papers (although it can be easily seen that some of them may be attributed to several parts simultaneously). The first part (quantum mathematics) combines the papers related to the methods generated by the concepts of quantization and quantum group. The second part is devoted to the theory of hypergroups and Lie hypergroups, which is one of the most important generalizations of the classical concept of locally compact group and of Lie group. A natural harmonic analysis arises on hypergroups, while any abstract transformation of Fourier type is gen­ erated by some hypergroup (commutative or not). Part III contains papers on the geometry of homogeneous spaces, Lie algebras and Lie superalgebras. Classical problems of the representation theory for Lie groups, as well as for topological groups and semigroups, are discussed in the papers of Part IV. Finally, the last part of the collection relates to applications of the ideas of Sophus Lie to differential equations.

Keywords

Cohomology Representation theory Sheaf cohomology algebra homology homomorphism manifold symplectic geometry

Editors and affiliations

  • B. P. Komrakov
    • 1
  • I. S. Krasil’shchik
    • 2
  • G. L. Litvinov
    • 3
  • A. B. Sossinsky
    • 4
  1. 1.International Sophus Lie CenterMinskBelarus
  2. 2.Moscow Institute for Municipal Economy and Diffiety InstituteMoscowRussia
  3. 3.Institute for New TechnologiesMoscowRussia
  4. 4.Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia

Bibliographic information