Background
Seligman, George Benham was born on April 30, 1927 in Attica, New York, United States. Son of George Frederick and Florence Rose (Benham) Seligman.
(This book deals with central simple Lie algebras over arb...)
This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. The book is intended for researchers and students of algebraic Lie theory, as well as for other researchers who are seeking explicit realizations of algebras or modules. It will probably be more useful as a resource to be dipped into, than as a text to be worked straight through.
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(The study of the structure of Lie algebras over arbitrary...)
The study of the structure of Lie algebras over arbitrary fields is now a little more than thirty years old. The first papers, to my know ledge, which undertook this study as an end in itself were those of JACOBSON (" Rational methods in the theory of Lie algebras ") in the Annals, and of LANDHERR ("Uber einfache Liesche Ringe") in the Hamburg Abhandlungen, both in 1935. Over fields of characteristic zero, these thirty years have seen the ideas and results inherited from LIE, KILLING, E. CARTAN and WEYL developed and given new depth, meaning and elegance by many contributors. Much of this work is presented in 47, 64, 128 and 234 of the bibliography. For those who find the rationalization for the study of Lie algebras in their connections with Lie groups, satisfying counterparts to these connections have been found over general non-modular fields, with the substitution of the formal groups of BOCHNER 40 (see also DIEUDONNE 108), or that of the algebraic linear groups of CHEVALLEY 71, for the usual Lie group. In particular, the relation with algebraic linear groups has stimulated the study of Lie algebras of linear transformations. When one admits to consideration Lie algebras over a base field of positive characteristic (such are the algebras to which the title of this monograph refers), he encounters a new and initially confusing scene.
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mathematician university professor
Seligman, George Benham was born on April 30, 1927 in Attica, New York, United States. Son of George Frederick and Florence Rose (Benham) Seligman.
Seligman received his bachelor"s degree in 1950 from the University of Rochester and his Doctor of Philosophy in 1954 from Yale University under Nathan Jacobson with thesis Lie algebras of prime characteristic. After he received his Doctor of Philosophy he was a Henry Burchard Fine Instructor at Princeton University from 1954–1956.
Instructor mathematics, Princeton (New Jersey) U., l954-56; instructor mathematics, Yale University, New Haven, l956-57; assistant professor, Yale University, New Haven, l957-60; associate professor, Yale University, New Haven, l960-65; professor, Yale University, New Haven, l965-82; James E. English professor, Yale University, New Haven, l982-97; professor emeritus, Yale University, New Haven, since 1997.
(The study of the structure of Lie algebras over arbitrary...)
(The study of the structure of Lie algebras over arbitrary...)
(This book deals with central simple Lie algebras over arb...)
With United States Naval Reserve, l945-46. Member American Mathematics Society (committee member), Mathematics Association American.
Married Irene Alice Schwieder, July 3l, l959. Children: Barbara, Karen.