I am trying to do some calculations and I don't understand what the output is.
L = lie_algebras.sp(QQ, 4)
L.gens()
The output is the following
(E[alpha[1]], E[alpha[2]], E[-alpha[1]], E[-alpha[2]], h1, h2)
I know that the command
L.gens()gives a set of genearators of the Lie algebra. So I understand that this is giving us an element from $e_\alpha\in L_\alpha$ for each $\alpha\in \Delta$ and the corresponding elements $h_\alpha \in H$, (where $\Delta$ is a base of the root system and $H$ is a Cartan Subalgebra). But I don't understand what these elements exactly are. Are these elements of a Chevalley basis?Let's say I want to figure out $\alpha_1(h_1)$. So I thought maybe
alpha1(h1)will give me the answer. But I am getting an error. I also triedL.alpha[1](h1)which results in an error as well. How can I fix this?
