For more than five decades Bertram Kostant has been one of the major architects of modern Lie theory. Virtually all his papers are pioneering with deep consequences, many giving rise to whole new fields of activities. His interests span a tremendous range of Lie theory, from differential geometry to representation theory, abstract algebra, and mathematical physics. Some specific topics cover algebraic groups and invariant theory, the geometry of homogeneous spaces, representation theory, geometric quantization and symplectic geometry, Lie algebra cohomology, Hamiltonian mechanics, modular forms, Whittaker theory, Toda lattice, and much more. It is striking to note that Lie theory (and symmetry in general) now occupies an ever increasing larger role in mathematics than it did in the fifties. This is the first volume (1955-1966) of a five-volume set of Bertram Kostant’s collected papers. A distinguished feature of this first volume is Kostant’s commentaries and summaries of his papers in his own words. Kostant’s work spans over 50 years, with his fundamental and varied contributions to many aspects of Lie theory, a subject pervading almost the whole of mathematics His interests span a tremendous range from differential geometry to representation theory, abstract algebra and mathematical physics Kostant’s papers demonstrate deep results, giving rise to whole new fields of activities. INDICE: From the contents Preface.- Bibliograph.- Curriculum Vitae.- Comments by Bertram Kostant on Papers in Volume I.- Holonomy and the Lie Algebra ofInfinitesimal Motions of a Riemannian Manifold, 1955.- On the Conjugacy of Real Cartan Subalgebras I, 1995.- On the Conjugacy of Real Cartan Subalgebras II, 1995.- On Invariant Skew Tensors, 1956.- On Differential Geometry and Homogeneous Spaces I, 1956.- On Differential Geometry and Homogeneous Spaces II, 1956.- On Holonomy and Homogeneous Spaces, 1957.- A Theorom of Frobenius, A Theorem of Amitsur--Levitski and Cohomology Theory, 1958.- A Characterization of the Classical Groups, 1958.- A Formula for the Multiplicity of a Weight, 1959.- The Three Dimensional Sub-Group and the Betti Numbers of a Complex Simple Lie Group, 1959.- A Characterization of Invariant Affine Connections, 1960.- Lie Algebra Cohomology and the Generalized Borel--Weil Theorem, 1961.- (with G. Hochschild and A. Rosenberg), Differential Forms of Regular Affine Algebras, 1962.
- ISBN: 978-0-387-09582-0
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 550
- Fecha Publicación: 01/11/2008
- Nº Volúmenes: 1
- Idioma: Inglés
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