Quantized Matrix Algebras and Quantum seeds

TL;DR

This paper explicitly constructs quantum seeds for certain quantized matrix algebras, analyzes their centers and block structures, and determines degrees at roots of unity, advancing understanding of their algebraic properties.

Contribution

It provides explicit quantum seeds for classes of quantized matrix algebras and explores their centers, block forms, and degrees at roots of unity, which was not previously known.

Findings

Explicit quantum seeds for quantized matrix algebras

Results on centers and block diagonal forms

Degrees determined at roots of unity

Abstract

We determine explicit quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centers and block diagonal forms {of these algebras.} In the case where $q$ is {an arbitrary} root of unity, this further determines the degrees.