That's the Way Things Spin Theoretically

Interesting ways of modeling ‘fundamental’ particles continue to develop along with algebras to use experimentally. The standard model of quantum physics doesn't use Octonion or Dixon algebra that could be valid ways of finding sharper descriptions of the way things spin.

https://en.wikipedia.org/wiki/Special_unitary_group

Spin and non-commutativity are important concepts about particles that may be represented algebraically

http://www.7stones.com/Homepage/_matter_dominant.pdf Geoffrey Dixon “The Standard Model arises from T := C⊗H⊗O”

The concept of finding deeper math that scientists can use is encouraging for those interested in learning how the mass-energy of this apparent Universe works. Hilbert space allows non-Euclidean extension of space representation to any number of dimensions. Algebraic representation of particles in any number of dimensions might be turbo-charged theoretically with new approaches.

https://en.wikipedia.org/wiki/Hilbert_space

https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

using Octonians to develop the standard model of physics particle-waves

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.86.025024 Unified theory of ideals

http://www.tunl.duke.edu/nnpss/lectures/19/NNPSS-I.pdf Fundamental symmetries of the standard model