The nilpotence of one of these structures is related to the nilpotence of other operators on a vector space by Engel's theorem.
The nilpotence of one of these structures is related to the nilpotence of other operators on a vector space by Engel's theorem. Assigning one of these to a Lie group defines a functor. One of these is solvable if its Killing form vanishes on its derived form by Cartan's first criteria. The exponential function can be used to generate a Lie group from one of these. These entities can be studied using Dynkin diagrams. These structures are skewsymmetric, bilinear and satisfy the Jacobi identity. A special class of these is named for Kac and Moody. For 10 points, name this type of vector space, named for a Norwegian.
The nilpotence of one of these structures is related to the nilpotence of other operators on a vector space by Engel's theorem.
Lie algebra