Has anyone worked out a uniform way of constructing the Hopf algebra of a Chevalley group out of the root system (or, more precisely out of the root datum for reductive groups).


By "uniform", I mean a method that works for any type, not case by case.


If yes, can anyone point out a reference in the literature? Ideally, I'd like to see the construction over the integers, but I'd still be interested in constructions over a field.



Hopf algebra of Chevalley group from the root system
A no-nonsense construction, over $Z$, following work of Kostant and Chevalley, is given in Lusztig's paper "Twelve bridges from a reductive group to its Langlands dual". The heart of the construction of the Hopf algebra is in Section 5. 


This is easy enough to find online, and according to Lusztig's webpage, it can also be found published in Contemp. Math. 478 (2009), 125-143.


Good luck!


