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## Homework Statement

I have the operators

##D_{\beta}:V_{\beta}\rightarrow V_{\beta}##

##R_{\beta\alpha 1}: V_{\beta} \otimes V_{\alpha 1} \rightarrow V_{\beta}\otimes V_{\alpha 1}##

##R_{\beta\alpha 2}: V_{\beta} \otimes V_{\alpha 2} \rightarrow V_{\beta}\otimes V_{\alpha 2}##

where each of the vector spaces are copies of ##\mathbb{C}^2##

## Homework Equations

## The Attempt at a Solution

I want to write the product ##D_{\beta}R_{\beta\alpha 1}R_{\beta\alpha 2}##, which makes sense on the space ##V_{\beta} \otimes V_{\alpha 1} \otimes V_{\alpha 2}##.

So I order to act on the full space I write ##D## as ##D_{\beta}\otimes I_{\alpha 1} \otimes I_{\alpha 2}##

and write ##R_{\beta\alpha 1}## as ##R_{\beta\alpha 1} \otimes I_{\alpha 2}##, where ##I_{\alpha 1}## and ##I_{\alpha 2}## are the identity operators in ##V_{\alpha 1}## and ##V_{\alpha 2}##.

My problem is that I don't know how to write ##R_{\beta\alpha 2}## since I'd basically have to stick and identity "in the middle".