Algebra and Operator Theory

1. Front Matter

   Pages i-viii

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2. On Leibniz Algebras

   • Sh. A. Ayupov, B. A. Omirov

   Pages 1-12

3. A Moduli Problem Related to Complex Supermanifolds

   • A. L. Onishchik

   Pages 13-24

4. Comparaison de L’Homologie de Hochschild et de L’Homologie de Poisson Pour Une Deformation des Surfaces de Klein

   • J. Alev, T. Lambre

   Pages 25-38

5. Quelques Resultats En K-Theorie Reelle

   • C. N. Costinescu

   Pages 39-48

6. Some Nilpotent Lie Algebras and Its Applications

   • M. Goze, Yu. Khakimdjanov

   Pages 49-64

7. Algebres de Lie Rigides

   • M. Goze, J. M. Ancochea Bermudez

   Pages 65-91

8. Family of p-Filiform Lie Algebras

   • J. M. Cabezas, J. R. Gómez, A. Jimenez-Merchán

   Pages 93-102

9. The Functional Representation of Commutative Symmetric Operator Algebras in Pontryagin Space

   • V. I. Chilin, S. Sh. Masharipova

   Pages 103-110

10. Continuous Decomposition of Real von Neumann Algebras of Type III

    • Sh. Usmanov

    Pages 111-116

11. Espaces Vectoriels Differentiels

    • Kamola Khakimdjanova

    Pages 117-126

12. Completude de L’equation D’Euler

    • Sh. Bromberg, A. Medina

    Pages 127-144

13. On Invariants of Second Order Linear Partial Differential Equations in Two Variables

    • U. Bekbaev

    Pages 145-156

14. Lattice-Ordered Groupoids and Their Prime Spectrums

    • Dj. Khadjiev, T. M. Shamilev

    Pages 157-164

15. Sur Un Probleme D’Elie Cartan

    • T. Hangan

    Pages 165-176

16. Classification of Non-Commutative Arens Algebras Associated with Semi-Finite Traces

    • R. Z. Abdullaev

    Pages 177-181

17. Order Unit Space of Type I _n with Banach Ball Property

    • M. A. Berdikulov

    Pages 183-186

18. On Markov Random Fields on UHF Algebras

    • N. N. Ganikhodzhaev, F. M. Mukhamedov

    Pages 187-192

19. Injectivity, Amenability, Semidiscreteness and Hyperfiniteness in Real W*-Algebras

    • A. Rakhimov, B. Boykabilov

    Pages 193-201

20. Contractive Projections on Facially Symmetric Spaces

    • N. J. Yadgorov, M. M. Ibragimov

    Pages 203-206

This volume presents the lectures given during the second French-Uzbek Colloquium on Algebra and Operator Theory which took place in Tashkent in 1997, at the Mathematical Institute of the Uzbekistan Academy of Sciences. Among the algebraic topics discussed here are deformation of Lie algebras, cohomology theory, the algebraic variety of the laws of Lie algebras, Euler equations on Lie algebras, Leibniz algebras, and real K-theory. Some contributions have a geometrical aspect, such as supermanifolds. The papers on operator theory deal with the study of certain types of operator algebras. This volume also contains a detailed introduction to the theory of quantum groups.
Audience: This book is intended for graduate students specialising in algebra, differential geometry, operator theory, and theoretical physics, and for researchers in mathematics and theoretical physics.

• Cohomology
• Lattice
• Operator theory
• Theoretical physics
• algebra
• algebraic varieties
• differential geometry
• manifold

• Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

  Yusupdjan Khakimdjanov, Shavkat A. Ayupov

• Department of Mathematics, Université de Haute Alsace, Mulhouse-Colmar, France

  Yusupdjan Khakimdjanov, Michel Goze

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