can anyone explain how commutators act on tri-vectors (in orthonormal conditions)? on bi-vectors i know that it ends up to be a bivector again, but with tri-vectors it vanishes if its lineraly dependent. what about the case if its not linearly dependent, does that mean it remains a tri-vector? how does a vector transform under a transformation generated by exponentiation of a trivector ? a transformation is a rotation or reflection, but who can explain the exponentiation?