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Lie groups and Lie algebras. Their representations, generalisations and applications. (English) Zbl 0886.00009
Mathematics and its Applications (Dordrecht). 433. Dordrecht: Kluwer Academic Publishers. vii, 442 p. (1998).
The articles of this volume will be reviewed individually.
Publisher’s description:
This collection brings together papers related to the classical ideas of Sophus Lie. The present work reflects the interests of scientists associated with the International Sophus Lie Center, and provides up-to-date results in Lie groups and Lie algebras, quantum mathematics, hypergroups, homogeneous spaces, Lie superalgebras, the theory of representations and applications to differential equations and integrable systems. Among the topics that are treated are quantization of Poisson structures, applications of multivalued groups, noncommutative aspects of hypergroups, homology invariants of homogeneous spaces, generalisations of the GodbillonVey invariant, relations between classical problems of linear analysis and representation theory, and the geometry of current groups.
Indexed articles:
Akueson, P.; Gurevich, D., Dual quasitriangular structures related to the Temperley-Lieb algebra, 1-16 [Zbl 0898.17010]
Donin, J., On the quantization of quadratic Poisson brackets on a polynomial algebra of four variables, 17-25 [Zbl 0974.17509]
Gurevich, D.; Donin, J.; Rubtsov, V., Two types of Poisson pencils and related quantum objects, 27-46 [Zbl 0973.81048]
Nazaikinskij, Vladimir; Sternin, Boris, Wave packet transform in symplectic geometry and asymptotic quantization, 47-69 [Zbl 0915.58108]
Zhelobenko, D. P., On quantum methods in the classical theory of representations, 71-84 [Zbl 0912.17004]
Buchstaber, V. M.; Rees, E. G., Multivalued groups, $$n$$-Hopf algebras and $$n$$-ring homomorphisms, 85-107 [Zbl 0903.20039]
Connett, William C.; Schwartz, Alan L., Hypergroups and differential equations, 109-115 [Zbl 0897.43005]
Gebuhrer, Marc-Olivier, Haar measure on locally compact hypergroups, 117-131 [Zbl 0895.43006]
Nessibi, M. M.; Sifi, M., Laguerre hypergroup and limit theorem, 133-145 [Zbl 0905.60016]
Osilenker, Boris P., The representation of the reproducing kernel in orthogonal polynomials on several intervals, 147-162 [Zbl 0901.42016]
Gilligan, Bruce, Homology invariants of homogeneous complex manifolds, 163-179 [Zbl 0899.53041]
Komrakov, Boris; Tchuryumov, Alexei, Micromodules, 181-198 [Zbl 0903.17005]
Onishchik, A. L., A spectral sequence for the tangent sheaf cohomology of a supermanifold, 199-215 [Zbl 0904.32005]
Razmyslov, Yu. P., On a duality of varieties of representations of ternary Lie and super Lie systems, 217-230 [Zbl 0914.17003]
Roger, Claude, Various aspects and generalizations of the Godbillon-Vey invariant, 231-247 [Zbl 1001.57047]
Roos, Guy, Volume of bounded symmetric domains and compactification of Jordan triple systems, 249-259 [Zbl 1009.17020]
Artemov, A. A., Asymptotic behavior of the Poisson transform on a hyperboloid of one sheet, 261-284 [Zbl 0904.43005]
Van Dijk, G.; Hille, S. C., Maximal degenerate representations, Berezin kernels and canonical representations, 285-298 [Zbl 0895.22008]
Mishchenko, Alexander S.; Mohammad, Noor, Asymptotic representation of discrete groups, 299-312 [Zbl 0909.22008]
Molchanov, V. F., Maximal degenerate series representations of the universal covering of the group $$SU(n,n)$$, 313-336 [Zbl 0899.22013]
Shtern, A. I., Almost representations and quasi-symmetry, 337-358 [Zbl 0896.22002]
Bolsinov, A. V.; Fomenko, A. T., Orbital isomorphism between two classical integrable systems, 359-382 [Zbl 0904.58024]
Demidov, E. E., Noncommutative deformation of the Kadomtsev-Petviashvili hierarchy and the universal Grassmann manifold, 383-391 [Zbl 0906.58003]
Dubrov, Boris; Komrakov, Boris, Symmetries of completely integrable distributions, 393-405 [Zbl 0906.58016]
Krasil’shchik, I. S., Algebras with flat connections and symmetries of differential equations, 407-424 [Zbl 0933.58022]
Lukatsky, A. M., On the geometry of current groups and a model of the Landau-Lifschitz equation, 425-433 [Zbl 0941.58006]
Smolyanov, O. G., Change of variable formulas for Gaussian integrals over spaces of paths in compact Riemannian manifolds, 435-442 [Zbl 0904.60038]
##### MSC:
 00B15 Collections of articles of miscellaneous specific interest 17-06 Proceedings, conferences, collections, etc. pertaining to nonassociative rings and algebras 22-06 Proceedings, conferences, collections, etc. pertaining to topological groups 81-06 Proceedings, conferences, collections, etc. pertaining to quantum theory 20-06 Proceedings, conferences, collections, etc. pertaining to group theory 58-06 Proceedings, conferences, collections, etc. pertaining to global analysis
##### Keywords:
Lie groups; Lie algebras; Representations; Generalisations