Yes! I've been looking for something like this for months now! A few weeks back, as this paper was being published, I remember a night where I was walking down the street wondering if such a thing was possible, to use some kind of tree structure to do efficient Clifford algebra products in higher dimensions. It must have been in the air :)
Consider that a Clifford algebra of a 15 dimensional vector space has an associated 2^15 = 32768 dimensional basis. To be able to do efficient calculations in arbitrary subspaces of such a huge algebra is amazing.
Consider that a Clifford algebra of a 15 dimensional vector space has an associated 2^15 = 32768 dimensional basis. To be able to do efficient calculations in arbitrary subspaces of such a huge algebra is amazing.
That said, higher dimensional Clifford algebras are related to lower ones by very well defined rules: https://en.wikipedia.org/wiki/Classification_of_Clifford_alg...