The Unique Decomposition Of Associative Color Algebra And The Cohomology Of Lie Color Algebra

This research method modded on the decomposition of associative algebra and the cohomology of associative superalgebra,conducted a study of associative color algebra and Lie color algebra.This paper is divided into three parts.The first part gives the proof the decomposition of associative color algebra and uniqueness.The second part gives a sufficient condition for the vanishing of the cohomology groups of an associative color algebra. The third part draws some conclusions of the cohomology of associative color algebra be extended to Lie color algebra.We can have some important identities.Theoreml:Let R be associative color algebra, andC(R)=0, let R have the decomposition R= R1⊕ncan not be divided,then m=n and through the new arrangeRi=Sii=1,2…m.Theorem2:Let S*denote the subalgebra without unity of A(?)FAoppwhich is generated by the elements of the formss withs∈S.Assume there is an element in S* acting invertibly on M.Then the restriction image of M)is 0 for every n.Theorem3:Let be a strong semisimple,finite dimensional Lie color algebra,charF=O,M is a dimensional L-module,then Hn(L,M)=0.