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GradedLieAlgebras :: axiomsLie

axiomsLie -- the axioms for Lie algebras

Description

The axioms depend on the sign of the generators, which are specified by 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.