Clifford Algebras for Projective and Conformal Geometry

Question

A Clifford Algebra over $\mathbb{R}^3$ may describe the rigid motions in space (namely, conjugation acts as a reflection by a plane).
A Clifford Algebra over $\mathbb{R}^4$ may describe the projective geometry in space.
A Clifford Algebra over $\mathbb{R}^5$ may describe the conformal geometry in space.

Where could be found an intuitive explanation for the last two items?

slehar · Accepted Answer · 2015-01-08 20:44:11Z

4

Scroll to the bottom of Clifford Algebra: A Visual Introduction, right under Clifford the Big Red Algebra and you will find two links:

If you like this intuitive graphical presentation of Clifford Algebra you might also be interested in another item by the same author

in monochrome pdf format, and there is a full color version of that paper here:

answered Jan 8, 2015 at 20:44

slehar

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$\begingroup$ As far as I have understood the role of Clifford Algebras in projective and conformal geometry, the metric information on the original vector space is lost after adding one or two more dimensions, because one only works with blades. Is that right? $\endgroup$
– Jjm
Jan 29, 2015 at 16:19

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rschwieb · Accepted Answer · 2015-01-15 19:55:17Z

2

Doran and Lasenby's book Geometric algebra for physicists does an OK job of presenting those three topics.

Normally the way physicists write does not make me very happy, but their exposition for these particular topics was very helpful to me.

answered Jan 15, 2015 at 19:55

rschwieb

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