Definition Of Lie Algebra

The name lie algebra was given by hermann weyl in the 1930s.

Definition of lie algebra. Then the axioms listed below are satisfied by the lie algebra. Lie algebra definition is a linear algebra which has the multiplicative operation denoted by and is bilinear such that aa bb c a a c b b c and a ab bc a a b b a c and satisfies the conditions that a a 0 and a b c b c a c a b 0 where a b c are any vectors in the vector space and a b c are scalars from the associated field. Meaning of lie algebra. What does lie algebra mean.

3 representations a representation of a lie algebra g is a lie algebra homomorphism from g to the lie algebra end v. Definitions definition of a lie algebra. Where xcan be canonically embedded into w x via the map. The free lie algebra on x is the lie subalgebra in tw x generated by x.

Holds bilinear mapping property axiom 2. If v is a lie algebra then the general linear lie algebra is denoted as. That is if then for all. Plural form of lie algebra.

Lie algebras were introduced to study the concept of infinitesimal transformations by marius sophus lie in the 1870s and independently discovered by wilhelm killing in the 1880s. For a lie algebra g and any x2g we de ne a map ad x. X w x x7 e x. Satisfies the jacobian identity.

Information and translations of lie algebra in the most comprehensive dictionary definitions resource on the web. Axioms of lie algebra.