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Collected Papers: Volume I 1955-1966 de Bertram Kostant

Collected Papers: Volume I 1955-1966

Autor Bertram Kostant Editat de Anthony Joseph, Shrawan Kumar, Michèle Vergne
en Limba Engleză Hardback – 6 aug 2009
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. 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. Now in the sixth decade of his career, he continues to produce results of astonishing beauty and significance for which he is invited to lecture all over the world.
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.
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Specificații

ISBN-13: 9780387095820
ISBN-10: 0387095829
Pagini: 518
Ilustrații: XX, 518 p. 1 illus.
Dimensiuni: 193 x 260 x 30 mm
Greutate: 1.23 kg
Ediția:2009
Editura: Springer
Colecția Springer
Locul publicării:New York, NY, United States

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Research

Descriere

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.
During his years as professor at the Massachusetts Institute of Technology from 1962 until retiring from teaching in 1993, he received many honors and prizes:  election to the National Academy of Sciences USA, the American Academy of Arts and Sciences, the AMS Steele Prize, Honorary Doctorates from University of Córdoba, Argentina, the University of Salamanca, Spain, Purdue University. Now in the sixth decade of his career, he continues to produce results of astonishing beauty and significance for which he is invited to lecture all over the world.
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.

Cuprins

Holonomy and the Lie Algebra of Infinitesimal Motions of A Riemannian Manifold.- On the Conjugacy of Real Cartan Subalgebras.- On the Conjugacy of Real Cartan Subalgebras II.- On INV Ariant Skew-Tensors.- On Differential Geomentry and Homogeneous Spaces. I..- On Differential Geometry and Homogeneous Spaces II.- On Holonomy and Homogeneous Spaces.- A Theorem of Frobenius, a Theorem of Amitsur-Levitski and Cohomology Theory.- A Characterization of the Classical Groups.- A Formula for the Multiplicity of a Weight.- The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group.- A Characterization of Invariant Affine Connections.- Lie Algebra Cohomology and the Generalized Borel-Weil Theorem.- Differential Forms on Regular Affine Algebras.- Differential Forms and Lie Algebra Cohomology for Algebraic Linear Groups.- Lie Group Representations On Polynomial Rings.- Lie Group Representations on Polynomial Rings.- Lie Algebra Cohomology and Generalized Schubert Cells.- Eigenvalues of a Laplacian and Commutative Lie Subalgebras.- Orbits, Symplectic Structures and Representation Theory.- Groups Over.

Caracteristici

Kostant is one of the leading architects of modern Lie theory
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.
Volume I contains Kostant’s summaries of his papers in his own words.
Volume I develops beautiful themes which are further elaborated in Volumes II-V
Includes supplementary material: sn.pub/extras

Notă biografică

Bertram Kostant was Professor Emeritus at MIT. He died on February 2, 2017 at 88 years old. Kostant was of one of the major architects of modern Lie theory and virtually all of his papers are pioneering with deep consequences, many giving rise to whole new fields of activities. His interests spanned a tremendous range of Lie theory, from differential geometry to representation theory, abstract algebra, and mathematical physics. He also had a long standing love affair with the icosahedron. Bertram Kostant was elected to the National Academy of Sciences in 1978, became a Sackler Institute Fellow at Tel Aviv University in 1982, received a medal from the College de France in 1983. In 2012 he became a Fellow of the American Mathematical Society. He was awarded the Steele Prize in 1990 for his paper On the existence and irreducibility of certain series of representations; paper #36 in Volume II of Kostant’s Collected Papers. In 2016 he received the Wigner Medal in Rio de Janeiro. During his mathematical career, Kostant received several honorary doctorates.

Textul de pe ultima copertă

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.
During his years as professor at the Masachusetts Institute of Technology from 1962 until retiring from teaching in 1993, he was elected to the National Academy of Sciences USA, the American Academy of Arts and Sciences, the AMS Steele Prize, Honorary Doctorates from University of Codoba, Argentina, the University of Salamanca, Spain, Purdue University. Now in the sixth decade of his career, he continues to produce results of astonishing beauty and significance for which he is invited to lecture all over the world.
This is the fourth volume (1991-2000) of a five-volume set of Bertram Kostant's collected papers. A distinguished feature of this fourth volume is Kostant's commentaries and summaries of his papers in his own words.