element4 said:
My knowledge of Lie groups/algebras are very limited, but in quantum physics this notation usually means commutator/anti-commutator (usually for bosons/fermions).
So
[A,B]_{-} = AB-BA
[A,B]_{+} = AB+BA
So i would guess, this is the same for the Lie Brackets.
Note that Lie-brackets are abstract things, which take two elements x and y and produce a new one [x, y].
In the section you are referring to, A and B are matrices and the square brackets are not Lie-brackets but simply commutators of matrices. For
those it is common to use the notation explained by element4.
Note that if we have a set of matrix
commutation relations
[T_i, T_j]_- = T_i T_j - T_j T_i = c_{ij}^k T_k
then we can "promote" them into a Lie-group whose algebra is defined by
[t_i, t_j] = c_{ij}^k t_k
where the brackets in the former refers to the matrix commutator and in the latter expression to the abstract operation called "Lie-bracket". The matrices T_i are one specific representation called the fundamental representation (if you remember that a representation is a function from the Lie-algebra to some subgroup of matrices, the fundamental representation would simply be the map t_i \to T_i linearly extended).
However, for a set of
anti-commutation relations this is not generally possible, as the Lie-bracket must satisfy a requirement
[t_i, t_j] = -[t_j, t_i]
which the matrix anti-commutator does not satisfy.
