The center of a quantized enveloping algebra at an even root of unity

TL;DR

This paper provides an explicit description of the center of a specialized quantized enveloping algebra at an even root of unity, extending previous work on the odd root case and highlighting the increased complexity.

Contribution

It offers a detailed characterization of the algebra's center at even roots of unity, filling a gap in the understanding of these algebraic structures.

Findings

Explicit description of the center at even roots of unity

Comparison with the odd root case showing increased complexity

Extension of De Concini-Kac-Procesi results

Abstract

We will give an explicit description of the center of the De Concini-Kac type specialization of a quantized enveloping algebra at an even root of unity. The case of an odd root of unity was already dealt with by De Concini-Kac-Procesi. Our description in the even case is similar to but a little more complicated than the odd case.