The Polynomial Identities and Invariants of N X N Matrices - Brossura

Formanek, Edward

Brossura

ISBN 10: 0821807307 ISBN 13: 9780821807309

Casa editrice: Amer Mathematical Society, 1991

Riassunto

The theory of polynomial identities, as a well-defined field of study, began with a well-known 1948 article of Kaplansky. The field has since developed along two branches: the structural, which investigates the properties of rings which satisfy a polynomial identity; and the varietal, which investigates the set of polynomials in the free ring which vanish under all specializations in a given ring. This book is based on lectures delivered during an NSF-CBMS Regional Conference, held at DePaul University in July 1990, at which the author was the principal lecturer. The first part of the book is concerned with polynomial identity rings. The emphasis is on those parts of the theory related to n x n matrices, including the major structure theorems and the construction of certain polynomials identities and central polynomials for n x n matrices. The ring of generic matrices and its centre is described. The author then moves on to the invariants of n x n matrices, beginning with the first and second fundamental theorems, which are used to describe the polynomial identities satisfied by n x n matrices. One of the exceptional features of this book is the way it emphasizes the connection between polynomial identities and invariants of n x n matrices. Accessible to those with background at the level of a first-year graduate course in algebra, this book gives readers an understanding of polynomial identity rings and invariant theory, as well as an indication of current problems and research in these areas.

Su questo libro

Contenuti

Polynomial identity rings; The standard polynomial and the Amitsur-Levitzki theorem; Central polynomials; Posner's theorem and the ring of generic matrices; The centre of the generic division ring; The Capelli polynomial and Artin's theorem; Representation theory of the symmetric and general linear groups; The first and second fundamental theorems of matrix invariants; Applications of the first and second fundamental theorems; The Nagata-Higman theorem and matrix invariants.

Dettagli dell?edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 1991
• ISBN 10: 0821807307
• ISBN 13: 9780821807309
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Contatto del produttore: non disponibile