How to define polynomial ring over noncommutative rings?
I want to study the algebra U+q(g)[x1,…,xn] where Uq(g) is the upper half quantum group of a simple lie algebra, and x1,…,xn are commutative variables. In Sagemath, it seems to me that the only way to construct Uq(g) is by using “Quantum Groups Using GAP’s QuaGroup Package”. But it does not support change ring or tensor product. Moreover, polynomial rings in SageMath have to be constructed over a commutative ring. How can I construct this algebra in SageMath?
This tutorial may help: https://sheaves.github.io/Noncommutat...