In this talk, we deals with the Casimir number of a rigid tensor category with finitely many isomorphism classes of indecomposable objects over an algebraically closed field k. The first part of this talk is concerned with the question when the Green algebra is Jacobson semi-simple. It turns out that the Green algebra is Jacobson semi-simple if and only if the Casimir number is not zero. In the second part we shall focus on the case where the tensor category is the representation category of a cyclic group G with order p over a field k with char k=p. In this case, the Casimir number is computable. This leads to a complete description of the Jacobson radical of the Green algebra.