Classical Groups and Geometric Algebra

Grove, Larry C.

ISBN 10: 0821820192 / ISBN 13: 9780821820193

Published by American Mathematical Society, Providence RI, 2002

About this Item

An ex-library copy in original laminated blue and yellow hard covers. The usual ex-libris markings. The binding is sound, the text is clean/unmarked, and there is little cover wear. No dust jacket, apparently as issued.

Seller Inventory # 062886

Bibliographic Details

• Title: Classical Groups and Geometric Algebra
• Publisher: American Mathematical Society, Providence RI
• Publication Date: 2002
• Language: English
• ISBN 10: 0821820192
• ISBN 13: 9780821820193
• Binding: Hardcover
• Edition: First Edition.
• Condition: Good
• Dust Jacket Condition: No Dust Jacket
• Book Type: Book

About this title

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.