Taking the derivative of the adjoint map gives the adjoint representation of the Lie algebra : Here is the Lie algebra o...
Under the Lie correspondence, nilpotent (respectively, solvable) connected Lie groups correspond to nilpotent (respectiv...
The universal cover of any connected Lie group is a simply connected Lie group, and conversely any connected Lie group i...
Examples The Jacobi identity is satisfied by the multiplication (bracket) operation on Lie algebras and Lie rings and th...
On the Lie algebra level, there is a corresponding linear mapping from the Lie algebra of G to End( V ) preserving the L...
Given again the finite-dimensional case, if bases have been chosen, then the composition of linear maps corresponds to t...
Group algebra over a finite group 4.1 Regular representation 4.2 Properties 4.3 Representations of a group algebra 4.4 C...
