Classical Groups and Geometric Algebra. (= Reihe: Graduate Studies in Mathematics (GSM), edited by Steven G. Krantz, David Saltman (Chair), David Sattinger and Ronald Stern, Volume 39). Erstausgabe.

Grove, Larry C.

ISBN 10: 0821820192 / ISBN 13: 9780821820193

Edité par American Mathematical Society, Providence, Rhode Island, 2002

A propos de cet article

Fadengehefteter glanzfolienkaschierter Pappeinband mit Rücken- und Deckeltitel. Der Einband mit einzelnen dezenten Kratzern, der Buchrücken lichtgebleicht, ansonsten guter bis sehr guter Erhaltungszustand. "A graduate-level text on the classical groups: groups of matrices, or (more often) quotients of matrix groups by small normal subgroups. It pulls together into a single source the basic facts about classical groups defined over fields, together with the required geometrical background information, from first principles. The chief prerequisites are basic linear algebra and abstract algebra, including fundamentals of group theory and some Galois Theory. The author teaches at the University of Arizona." (Verlagstext) In englischer Sprache. X, 169, (5) pages. 4° (182 x 260mm).

N° de réf. du vendeur BN32874

Détails bibliographiques

• Titre: Classical Groups and Geometric Algebra. (= Reihe: Graduate Studies in Mathematics (GSM), edited by Steven G. Krantz, David Saltman (Chair), David Sattinger and Ronald Stern, Volume 39). Erstausgabe.
• Éditeur: American Mathematical Society, Providence, Rhode Island
• Date de parution: 2002
• Langue: anglais
• ISBN à 10 chiffres: 0821820192
• ISBN à 13 chiffres: 9780821820193
• Reliure: Hardcover/gebunden
• Édition: First Printing.
• État de l'article: gut
• Poids: 550 grammes

A propos de ce titre

Synopsis

'Classical groups', named so by Hermann Weyl, are groups of matrices or quotients of matrix groups by small normal subgroups. Thus the story begins, as Weyl suggested, with 'Her All-embracing Majesty', the general linear group $GL_n(V)$ of all invertible linear transformations of a vector space $V$ over a field $F$. All further groups discussed are either subgroups of $GL_n(V)$ or closely related quotient groups. Most of the classical groups consist of invertible linear transformations that respect a bilinear form having some geometric significance, e.g., a quadratic form, a symplectic form, etc. Accordingly, the author develops the required geometric notions, albeit from an algebraic point of view, as the end results should apply to vector spaces over more-or-less arbitrary fields, finite or infinite. The classical groups have proved to be important in a wide variety of venues, ranging from physics to geometry and far beyond.In recent years, they have played a prominent role in the classification of the finite simple groups. This text provides a single source for the basic facts about the classical groups and also includes the required geometrical background information from the first principles. It is intended for graduate students who have completed standard courses in linear algebra and abstract algebra. The author, L. C. Grove, is a well-known expert who has published extensively in the subject area.