| LR algebra is an important non-associative algebra, its commutator satisfiesJacobi equation. Therefore, LR algebra is a Lie-admissible algebra, is also emergingconcept now[1]. linked with the Lie algebra. LR algebra's definition is proposed byD.Burde, K.Dekimpe and S.Deschamps[2].A LR algebras is a vector space over a field K with a bilinear product(x, y)→xy satisfyingx·(y·z)=y·(x·z)(x·y)·z=(x·z)·yfor x1, x2, x3∈A.Lie algebra's theory and method has penetrated into many areas of mathematicsand theoretical physics. This article discusses LR algebra which is a Lie-admissibleAlgebra. This algebraic system is widely used in many areas of geometry, algebraand physics.In this paper, we classify some of the LR algebra, and have achieve some LRalgebra. In chapter1, the development of the LR algebra is brief introduced. Inchapter2, LR algebra definition and related definitions and examples are given. Inchapter3, some properties of LR algebra are listed. In chapter4, portray some ofthe LR algebra which includes on the classification and achievement of certain LRalgebra. |
