Lie algebra and classefection

Post-Lie algebras were introduced by Valette in relation to the disintegration homologies of the posets and various studies were carried out on them. Pre-Lie algebras play an important role in many areas, especially geometry and physics. The post-lie algebraic structure for the Lie algebra pair (L; n) is examined, and the post-lie algebra entity criterion for semi-simplicity and solvability has been investigated by revising the Burde (2009), Burde (2016) and Burde (2012) techniques. The concept of the N-derivative is a natural generalization of the derivative and the 3-dimension derivative concept. Let L be a Lie algebra rated by a Cartan subtype of finite dimension. The N-derivative algebra and the N-derivative algebraic relation have been studied and the conditions for overlapping Lian ve Chen (2016) have been reported. Schrdinger-Virasora algebra, Kac-Moody algebra. In addition, (elfa;beta ;gama ) - derivative concept and its properties have been investigated for simple algebras. It has been determined that post-Lie algebraic structure can be classifiedusing generalized derivatives. A post-Lie algebra is a generalization of pre-Lie algebra.