Clifford Algebras

Question

What would be the best source to learn Clifford Algebras from? Anything online would suffice or any textual sources for that matter..

I'm interested in doing a project in the subject, but I'm not sure where to begin to learn. What would be the prerequisites to ensure a stable foundation?

Thanks

I'm also aware that they can be applied to Digital Imagining Processing

Are you interested in Clifford algebras in their own right (i.e. just the algebraic theory), or would you prefer to work towards an application, such as spin geometry? — Henry T. Horton, Aug 01 '13 at 05:26
@HenryT.Horton Anything that constitutes publishable research — Anthony Peter, Aug 01 '13 at 05:29
@HenryT.Horton However, I'd probably prefer just the pure algebraic theory — Anthony Peter, Aug 01 '13 at 05:37
It would be good if you had a fair chunk of abstract algebra under your belt already, or else were prepared to pick it up along the way. You would at least need to have a good grasp of linear algebra. It's not really possible to study Clifford algebra s in isolation. — rschwieb, Aug 01 '13 at 11:26
I have telegram channel with podcasts about Clifford Algebra t.me/deep_dive_math — Vyacheslav Loginov, Feb 17 '25 at 13:50

Amitesh Datta · Answer 1 · 2013-08-01T06:58:20.677

Clifford algebras arise in several mathematical contexts (e.g., spin geometry, abstract algebra, algebraic topology etc.). If you're just interested in the algebraic theory, then the prerequisites would probably be a solid background in abstract algebra. For example, I think linear algebra and ring theory are prerequisites but in practice, one should probably know more (e.g., for motivation and mathematical maturity). If you could elaborate further on your mathematical background, then I'm happy to provide more detailed suggestions.

I think this link provides a nice elementary introduction to Clifford algebras: http://www.av8n.com/physics/clifford-intro.htm. If that's too basic for you, then also have a look at: http://www.fuw.edu.pl/~amt/amt2.pdf. If you're familiar with algebraic topology, then the following paper is very interesting: http://www.ma.utexas.edu/users/dafr/Index/ABS.pdf.

I have a mathematical background in both Linear Algebra as well as Abstract Algebra — Anthony Peter, Aug 01 '13 at 06:53

score 4 · Accepted Answer · edited Dec 03 '20 at 18:08

When first starting out, I found some of Alan Macdonald's introductory material to "geometric algebra" very useful for developing intuition.

To make a gross overgeneralization, geometric algebras are basically the low dimensional Clifford algebras over $\Bbb R$ that are most relevant to 2-d and 3-d geometry, and even some 4-d relativistic geometry. I think it's beneficial to have that experience before seeing more general Clifford algebras over different fields, with higher dimensions, with different forms, etc.

I found that paper and several of the other papers he has online very helpful. There is a more technical description, along with some practical uses, in Jacobsons Basic Algebra II.

Slightly more physics-y versions of the same content are found here. I have not had the opportunity to read it, but Lundholm's material is also something I see frequently suggested.

Clifford Algebras

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