The Center of Small Quantum Groups I: The Principal Block in Type A
The Center of Small Quantum Groups I: The Principal Block in Type A
We develop an elementary algebraic method to compute the center of the principal block of a small quantum group associated with a complex semisimple Lie algebra at a root of unity. The exemplary case of $\mathfrak{sl}_3$ is computed explicitly, and further evidence of $\mathfrak{sl}_4$ is sketched. This allows us to …