William Talbot

Yes @joansola that seems right to me. I didn't realise that before, and i can use `( a.hat() * b.hat() - b.hat() * a.hat() ).vee()` in the meantime for my...

One additional note is that it would be convenient to have a lie bracket function on the lie algebra elements themselves, which would avoid recomputation / unnecessary mapping to/from the...

An additional note is that the lie bracket also equals $[X, Y] = adj(X)Y = XY - YX$. where $adj$ is the small adjoint. See section 10.2.6 equation 10.37 of...

Perhaps the lie bracket could be implemented something like: ``` TangentBase::LieAlg TangentBase::lieBracket(TangentBase rhs) { return TangentBase(smallAdj() * rhs.coeffs()).hat(); } ``` In equation form, this is $(\text{adj}(l^{\wedge}) r)^{\wedge}$, which I'm pretty...

Ok so it seems like the final decision was to make the lie algebra `x^ = x.hat() = [0 x ; 0 0]`? This makes sense to me (admittedly with...