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GradedLieAlgebras :: axiomsLie

axiomsLie -- the axioms for Lie algebras

Description

The axioms depend on the signs of the generators, which are specified by lieAlgebra(..., genSigns => ...). The sign of an element can be obtained by the function signLie, in the axioms below the sign of an element a is written sign(a).

Anticommutativity: [a,b] = -(-1)sign(a) * sign(b) [b,a]

Jacobi identity: [a,[b,c]] = [[a,b],c] + (-1)sign(a) * sign(b) [b,[a,c]]

Also, in characteristic 2 and 3, there are in addition the following axioms:

Characteristic 2: [a,a] = 0

Characteristic 3: [a,[a,a]] = 0

For the programmer

The object axiomsLie is a symbol.