Research Paper#Quantum Groups, Hopf Algebras, Representation Theory🔬 ResearchAnalyzed: Jan 3, 2026 16:04
Quantum Group Structure and Properties at Roots of Unity
Published:Dec 29, 2025 14:39
•1 min read
•ArXiv
Analysis
This paper investigates the structure of Drinfeld-Jimbo quantum groups at roots of unity, focusing on skew-commutative subalgebras and Hopf ideals. It extends existing results, particularly those of De Concini-Kac-Procesi, by considering even orders of the root of unity, non-simply laced Lie types, and minimal ground rings. The work provides a rigorous construction of restricted quantum groups and offers computationally explicit descriptions without relying on Poisson structures. The paper's significance lies in its generalization of existing theory and its contribution to the understanding of quantum groups, particularly in the context of representation theory and algebraic geometry.
Key Takeaways
- •Classifies centrality and commutativity of skew-polynomial algebras.
- •Constructs and analyzes a family of Hopf ideals related to Weyl group elements.
- •Provides a rigorous construction of restricted quantum groups.
- •Extends results to even orders of the root of unity and non-simply laced Lie types.
- •Offers computationally explicit descriptions without Poisson structures.
Reference
“The paper classifies the centrality and commutativity of skew-polynomial algebras depending on the Lie type and the order of the root of unity.”