FTP, identify this type of vector space over a field which is not necessarily associative but is bilinear and satisfies the Jacobi identity.
The semi-simple types are classified by the root systems of their Cartan subalgebras, or maximal toruses, and an Abelian subalgebra of this type is also known as a torus. One is solvable if the lower central series converges to zero, and a maximal solvable type is called a Borel subalgebra. Vector fields on a differentiable manifold form an infinite-dimensional one, and Euclidean space becomes one if we allow the bracket operator to equal the cross product of vectors. FTP, identify this type of vector space over a field which is not necessarily associative but is bilinear and satisfies the Jacobi identity.
The semi-simple types are classified by the root systems of their Cartan subalgebras, or maximal toruses, and an Abelian subalgebra of this type is also known as a torus.
Lie(LEE) algebra