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Mathematical biology

Mathematical biology BOOK REVIEWS 195 order 3 by J. Tits [5] in the finite case in his construction of the family of finite simple groups G2 and of the only known families of finite generalized hexagons). Crumeyrolle begins by restricting the characteristic to be different from 2, so the bilinear form B can be replaced by B/2, as is traditional in the theory of quadratic forms. But he generalizes to allow alternating forms, and thus brings in the symplectic Clifford algebras. Much of the theory remains more or less the same. Then he restricts K to be the reals or the complexes. (The applications he has in mind are primarily to quantum mechanics, so this restriction is quite natural and does allow some simplifications.) He generalizes the triality principle to allow at least certain other dimensions. And he brings in differential manifolds and Lie groups. There seems to be no end to the machinery that is erected, but throughout the exposition the author remains lucid and sympathetic to the reader. There are misprints, of course, but we noticed none that appeared to leave the meaning in doubt. The author has written a treatise on Clifford algebras (and their symplectic analogues) that http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Mathematical biology

Acta Applicandae Mathematicae , Volume 23 (2) – May 4, 2004

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References (68)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00048808
Publisher site
See Article on Publisher Site

Abstract

BOOK REVIEWS 195 order 3 by J. Tits [5] in the finite case in his construction of the family of finite simple groups G2 and of the only known families of finite generalized hexagons). Crumeyrolle begins by restricting the characteristic to be different from 2, so the bilinear form B can be replaced by B/2, as is traditional in the theory of quadratic forms. But he generalizes to allow alternating forms, and thus brings in the symplectic Clifford algebras. Much of the theory remains more or less the same. Then he restricts K to be the reals or the complexes. (The applications he has in mind are primarily to quantum mechanics, so this restriction is quite natural and does allow some simplifications.) He generalizes the triality principle to allow at least certain other dimensions. And he brings in differential manifolds and Lie groups. There seems to be no end to the machinery that is erected, but throughout the exposition the author remains lucid and sympathetic to the reader. There are misprints, of course, but we noticed none that appeared to leave the meaning in doubt. The author has written a treatise on Clifford algebras (and their symplectic analogues) that

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: May 4, 2004

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