mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, a quasi-Lie algebra in abstract algebra is just like a

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...

, but with the usual

axiom An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or f ...

,x 0

replaced by :

,y -,x /math> (anti-symmetry).

In characteristic other than 2, these are equivalent (in the presence of bilinearity), so this distinction doesn't arise when considering real or complex Lie algebras. It can however become important, when considering ''Lie algebras'' over the integers.

In a quasi-Lie algebra,

: 2,x 0. Therefore, the bracket of any element with itself is 2-torsion, if it does not actually vanish.

References

* Lie algebras {{algebra-stub

See also

References