On quaternions and octonions : their geometry, arithmetic, and symmetry / John H. Conway, Derek A. Smith.

Format:

Book

Author/Creator:

Conway, John H. (John Horton)

Contributor:

Smith, Derek Alan, 1970-

Language:

English

Subjects (All):

Quaternions.

Cayley numbers (Algebra).

Physical Description:

xii, 159 p. : ill.

Edition:

First edition.

Place of Publication:

Natick, Mass. : AK Peters, c2003.

Language Note:

English

Summary:

"This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less familiar octonion algebra, concentrating on its remarkable "triality symmetry" after an appropriate study of Moufang loops. The authors also describe the arithmetics of the quaternions and octonions. The book concludes with a new theory of octonion factorization. Topics covered include the geometry of complex numbers, quaternions and 3-dimensional groups, quaternions and 4-dimensional groups, Hurwitz integral quaternions, composition algebras, Moufang loops, octonions and 8-dimensional geometry, integral octonions, and the octonion projective plane."--Provided by publisher.

Contents:

chapter I I The Complex Numbers

chapter II II The Quaternions

chapter III III The Octonions.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. 149-152) and index.

Description based on metadata supplied by the publisher and other sources.

ISBN:

9781000687774

1000687775

9780429185861

0429185863

9781439864180

1439864187

OCLC:

922955594