Questions about Lie algebra
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 eα∈Lα for each α∈Δ and the corresponding elements hα∈H, (where Δ 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 α1(h1). 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?