Research On Hom - Lie Algebra

Because of the dual need of physical and Lie algebra, People began to study Hom-Lie algebra and take it as part of a study of deformations of the Witt and the Virasoro algebras. Some Properties of Hom-Lie are cited by many important alge-bras, As we all know, Hom-Lie algebra is algebra’s promotion, For the Lie algebra, we can study its derivations and center expansion, etc. For the Hom-Lie algebra, we can also research in these areas. This paper studies the derivations and center expansion of Hom-Lie algebra (gl(2,C),α).This paper firstly describes the background, significance and development of Hom-Lie algebra. Secondly, recall some basic knowledges and introduce some rele-vant Theorems and conclusions of derivation algebra of Hom-Lie algebra (gl(2,C). Finally, recall the concept of2-cocycle and define the center of the expansion of Hom-Lie algebra, prove its center expansion is trivial.