Lie Groups and Lie Algebras: Their Representations, Generalisations and Applications
B.P. Komrakov, I.S. Krasil'shchik, G.L. Litvinov, A.B. Sossinsky
Springer Netherlands, Mar 31, 1998 - Mathematics - 447 pages
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.
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action Applications associated associative algebra assume Banach space base basis bounded bracket bundle called classical closed cohomology coincides commutative compact complex condition connected consider construct continuous corresponding defined Definition denote derivative described determined differential dual element equal equation equivalent example exists fact field finite fixed formula functions given gives group G Hence homogeneous homomorphism hypergroup identity integral introduce invariant irreducible ISBN isomorphic Lemma Lie algebra Lie group linear locally manifold mapping Math Mathematics matrix means measure module multiplication namely natural objects obtain operator orbits pair particular Poisson polynomials positive problem Proof properties Proposition prove quantization quantum quantum mechanics quasi-representations reduced relations representation respect result satisfying Shtern simple space structure subgroup symmetric ternary Theorem theory topological transform University values vector weight