How to define polynomial ring over noncommutative rings?

asked 2024-03-14 15:15:31 +0200

I want to study the algebra $$U_q^+(\mathfrak{g})[x_1,\ldots,x_n]$$ where $U_q(\mathfrak{g})$ is the upper half quantum group of a simple lie algebra, and $x_1,\ldots,x_n$ are commutative variables. In Sagemath, it seems to me that the only way to construct $U_q(\mathfrak{g})$ 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?

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Max Alekseyev gravatar imageMax Alekseyev ( 2024-03-14 17:17:40 +0200 )edit