It is essentially Majid'e method (so-called Double bosonization) but handier. But everything is defined to be found rather than be discovered (it is discovered, but to make it looks natural to be found is a part of voluntary work of mathematicians). 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

(the following from Jantzen, one of the best book for Quantum groups)