Analysis of Uq(sl(m+1))-symmetries on quantum n-spaces

TL;DR

This paper investigates how the quantum group $U_q(sl(m+1))$ acts as symmetries on quantum n-spaces, providing a complete characterization for low dimensions and extending to higher dimensions.

Contribution

It classifies all module-algebra structures of $U_q(sl(m+1))$ on quantum spaces for specific low dimensions and discusses general cases for larger n.

Findings

Complete classification for $A_q(2)$ and $A_q(3)$

Extension of module-algebra structures to $A_q(n)$ for $n \\geq 4$

Framework for understanding quantum group symmetries on quantum spaces

Abstract

In this paper, the module-algebra structures of $U_q(sl(m+1))$ on the quantum $n$-space $A_q(n)$ are studied. We characterize all module-algebra structures of $U_q(sl(m+1))$ on $A_q(2)$ and $A_q(3)$ when $m\geq 2$. The module-algebra structures of $U_q(sl(m+1))$ on $A_q(n)$ are also considered for any $n\geq 4$.