The STA gauge theory of gravity substitues STA-multivector-valued linear functions of STA-multivectors for the rank 4 tensors of the usual treatment of GR. That is a quantity of (24×24=)256 real degrees of freedom.
I wonder if these quantities could be replaced by single multivectors in a geometric algebra with 8 basis vectors. These also have (28=)256 degrees of freedom, but they might make the equations simpler.
This would mean having a second set of 4 basis vectors in addition to the normal 4 (North, West, Up and Stopped). I wonder what the physical interpretation of these vectors would be? (Some sort of dual vectors perhaps?) Would they obey the normal rules of geometric algebra or would some generalization be required (perhaps to non-associativity like in the octonions or sedenions).