Build Backlinks to Amazon product page

I have a physical product that I sell on Amazon. I am not the only seller of the product but I am the manufacture of it so when it sells I always make money.

My question is, can I send back links to the main amazon selling page? Will I get any benefits out of it? Amazon has optimized it for a few good keywords that would defiantly help with sales if it was raked higher.

Has anyone tried this? I would think Amazon would love this, even low quality back links.