Talk:Tensor algebra

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I removed the following statement:

To have the complete algebra of tensors, contravariant as well as covariant, one should take T(W) where W is the direct sum of V and its dual space - this will consist of all tensors T_I^J with upper indices J and lower indices I, in classical notation.

Classically, a tensor over V is an element of V⊗...⊗V⊗V^*⊗...⊗V^*; with the construction given above, one would also get mixed terms such as V⊗V^*⊗V. To get the true algebra of all classical tensors, one would have to impose relations so that the elements of V commute with those of V^*. 21:13, 5 Sep 2004 (UTC)