Advances in Analysis and Geometry

. Ed(s): Qian, Tao; Hempfling, Thomas; McIntosh, Alan; Sommen, Frank; Sommen, Franciscus

ISBN 10: 3764366613 / ISBN 13: 9783764366612

Published by Birkhauser Verlag AG, 2004

About this Item

At the heart of Clifford analysis is the study of systems of special partial differential operators that arise naturally from the use of Clifford algebra as a calculus tool. This book focuses on the study of Dirac operators and related ones, together with applications in mathematics, physics and engineering. Editor(s): Qian, Tao; Hempfling, Thomas; McIntosh, Alan; Sommen, Frank; Sommen, Franciscus. Series: Trends in Mathematics. Num Pages: 391 pages, biography. BIC Classification: PBF. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 235 x 155 x 25. Weight in Grams: 830. . 2004. Hardback. . . . . Books ship from the US and Ireland.

Seller Inventory # V9783764366612

Bibliographic Details

• Title: Advances in Analysis and Geometry
• Publisher: Birkhauser Verlag AG
• Publication Date: 2004
• Language: English
• ISBN 10: 3764366613
• ISBN 13: 9783764366612
• Binding: Hardcover
• Condition: New

About this title

Synopsis

On the 16th of October 1843, Sir William R. Hamilton made the discovery of the quaternion algebra H = qo + qli + q2j + q3k whereby the product is determined by the defining relations ·2 ·2 1 Z =] = - , ij = -ji = k. In fact he was inspired by the beautiful geometric model of the complex numbers in which rotations are represented by simple multiplications z ----t az. His goal was to obtain an algebra structure for three dimensional visual space with in particular the possibility of representing all spatial rotations by algebra multiplications and since 1835 he started looking for generalized complex numbers (hypercomplex numbers) of the form a + bi + cj. It hence took him a long time to accept that a fourth dimension was necessary and that commutativity couldn't be kept and he wondered about a possible real life meaning of this fourth dimension which he identified with the scalar part qo as opposed to the vector part ql i + q2j + q3k which represents a point in space.