Advances in Analysis and Geometry
New Developments Using Clifford Algebras
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Beschreibung
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.
Contains most recent results and surveys of the state of the art in the discipline Based on an ICM 2002 Satellite Meeting on Clifford Analysis and Its Applications in Macau
This volume is dedicated to analytic and geometric aspects of Clifford analysis and its applications. There are two sources of papers in this collection. One is a satellite conference to the ICM 2002 in Beijing, held August 15-18 at the University of Macau; and the other source are invited contributions by experts in the field. All articles were strictly refereed and contain previously unpublished new results, some include comprehensive surveys. Including applications to articificial intelligence, number theory, numerical analysis and physics, the book will be a unique resource for postgraduates and researchers in a large number of disciplines.
Autor*in
Tao Qian
Themen in »Advances in Analysis and Geometry«
Algebra Clifford algebras Clifford analysis Cohomology Distribution Elliptic functions Hypermonogenic functions Mathematical physics Operator theory Spinor geometry calculus