IdentityMatrix for abstract tensor

[Yi Wang]

Dear all,

I was trying to make use of the abstract tensors that are introduced in Mathematica 9. I would need to be able to construct an identity matrix such that (for a general dimension):

TensorContract[A=E2=8A=97IdentityMatrix, {{2,3}}]//TensorReduce (* or any other simplification *)

gives A,

TensorContract[A=E2=8A=97IdentityMatrix=E2=8A=97B=E2=8A=97..., {{2,3}}]//TensorReduce

gives A=E2=8A=97B=E2=8A=97..., and

TensorContract[IdentityMatrix, {{1,2}}]//TensorReduce

gives TensorDimensions[e].

Is it possible to implement something like this? Thanks!