On The Order And Index Of Tensor Category

In this article,we first give the definitions of tensor category and quasi-Hopf algebra,and then we prove the representation category of quasi-Hopf alge-bras is a tensor category.Then we generalized the definitions of the order and index which given by Yong-chang Zhu etc.(see cf.[32]).to the tensor category,and we prove that the order and index of tensor category are two invariants.Furthermore,we prove various divisibility and integrality results for the two invariants about the representation category of semisimple Hopf algebras.Finally,we prove our definitions about order and index are indeed to generalize the definitions given by Yong-chang Zhu etc.(cf.[32]).