Geometric Algebra for Physicists Anthony Lasenby, Chris Doran
Publisher: Cambridge University Press

This Demonstration displays the classification of real Clifford algebras, making the eightfold periodicity manifest by mapping it onto a clock created from the eight trigrams used in the I Ching. We may always depend on it that algebra,. I studied category theory a bit here at Columbia from Lauda, and took some representation theory with Khovanov, but I think (at least at this point in time) my calling in physics is geometrical algebras. The case of most interest in physics is V=mathbf R^4, (cdot,cdot) the Minkowski inner product of signature (3,1). Baez, "Octonions," Bulletin of the American Mathematical Society, 39, 2002 pp. The theory of Clifford algebras for real vector spaces V is rather complicated. Which cannot be translated into good English. In my previous post I wrote about Geometric Algebra generalities. Matrix representation for tridimensional space geometric algebra. "Clifford Algebras in Physics." (2005) http://arxiv.org/ abs/hep-th/0506011. We saw that the tridimensional space generate a geometric algebra of dimension (2^3 = 8 = 1 + 3 + 3 + 1) composed of four linear spaces: scalars, vectors, bivectors and pseudo-scalars. Clifford, "On the Classification of Geometric Algebras," Mathematical Papers of W. Clifford Common Sense in the Exact Sciences *VFR Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour, with interesting applications in contemporary mathematical physics and geometry. Francesco's notes about Maths, Physics, Computer Science Saturday, May 11, 2013.