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Lie Groups and Lie Algebras

Their Representations, Generalisations and Applications

  • Book
  • © 1998

Overview

Editors:
  1. B. P. Komrakov

    1. International Sophus Lie Center, Minsk, Belarus

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  2. I. S. Krasil’shchik

    1. Moscow Institute for Municipal Economy and Diffiety Institute, Moscow, Russia

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  3. G. L. Litvinov

    1. Institute for New Technologies, Moscow, Russia

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  4. A. B. Sossinsky

    1. Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

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

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Table of contents (27 chapters)

  1. Front Matter

    Pages i-vii
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  3. Hypergroups

    1. Front Matter

      Pages 85-85
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    2. Multivalued Groups, n-Hopf Algebras and n-Ring Homomorphisms

      • V. M. Buchstaber, E. G. Rees
      Pages 85-107

    3. Hypergroups and Differential Equations

      • William C. Connett, Alan L. Schwartz
      Pages 109-115

    4. Haar Measure on Locally Compact Hypergroups

      • Marc-Olivier Gebuhrer
      Pages 117-131

    5. Laguerre Hypergroup and Limit Theorem

      • M. M. Nessibi, M. Sifi
      Pages 133-145

    6. The Representation of The Reproducing Kernel in Orthogonal Polynomials on Several Intervals

      • Boris P. Osilenker
      Pages 147-162

  4. Homogenious Spaces And Lie Algebras and Superalgebras

    1. Front Matter

      Pages 163-163
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  5. Homogenious Spaces and Lie Algebras and Superalgebras

    1. Homology Invariants of Homogeneous Complex Manifolds

      • Bruce Gilligan
      Pages 163-179

    2. Micromodules

      • Boris Komrakov, Alexei Tchuryumov
      Pages 181-198

    3. A Spectral Sequence for the Tangent Sheaf Cohomology of a Supermanifold

      • A. L. Onishchik
      Pages 199-215

    4. On a Duality of Varieties of Representations of Ternary Lie and Super Lie Systems

      • Yu. P. Razmyslov
      Pages 217-230

    5. Various Aspects and Generalizations of the Godbillon-Vey Invariant

      • Claude Roger
      Pages 231-247

    6. Volume of Bounded Symmetric Domains and Compactification of Jordan Triple Systems

      • Guy Roos
      Pages 249-259
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Keywords

About this book

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.

Editors and Affiliations

  • International Sophus Lie Center, Minsk, Belarus

    B. P. Komrakov

  • Moscow Institute for Municipal Economy and Diffiety Institute, Moscow, Russia

    I. S. Krasil’shchik

  • Institute for New Technologies, Moscow, Russia

    G. L. Litvinov

  • Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    A. B. Sossinsky

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