Baez wrote some ideas in [1], one I'm liking connects Lorentz group in dimensions 3,4,6 and 10 with the modular group SL(2,Z) that is at a crossroads of several hardcore math themes. For Lie algebras:

sl(2, R) ≅ so(2,1)

sl(2, C) ≅ so(3,1)

sl(2, H) ≅ so(5,1)

sl(2, O) ≅ so(9,1)

Dirac equation is the C case, the other cases have their uses.

[1] https://arxiv.org/abs/math/0105155