Lie Groups and Lie Algebras

1. Front Matter

   Pages i-vii

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2. Quantum Mathematics

   1. Front Matter

      Pages 1-1

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   2. Dual Quasitriangular Structures Related to the Temperley-Lieb Algebra

      • P. Akueson, D. Gurevich

      Pages 1-16

   3. On The Quantization of Quadratic Poisson Brackets on a Polynomial Algebra of Four Variables

      • J. Donin

      Pages 17-25

   4. Two Types of Poisson Pencils and Related Quantum Objects

      • D. Gurevich, J. Donin, V. Rubtsov

      Pages 27-46

   5. Wave Packet Transform in Symplectic Geometry and Asymptotic Quantization

      • Vladimir Nazaikinskii, Boris Sternin

      Pages 47-69

   6. On Quantum Methods in the Classical Theory of Representations

      • D. P. Zhelobenko

      Pages 71-84

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

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.

• Cohomology
• Representation theory
• Sheaf cohomology
• algebra
• homology
• homomorphism
• manifold
• symplectic geometry
• partial differential equations

• 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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