Hacker News Reader

Is there some canonical metric on Lie algebras that makes this possible? Otherwise geometric algebra won't get you far.

Every Lie algebra is a bivector algebra (see 'Lie groups as Spin groups' http://geocalc.clas.asu.edu/pdf/LGasSG.pdf).

Additionally the GA formalism enables closed form solutions for the exponential map for all bivector algebras. (see 'Graded symmetry Groups' https://www.researchgate.net/publication/353116859_Graded_Sy...).