On simple modules and automorphisms of the quantum Galilei group

Abstract

This paper is devoted to ring theoretic properties and representations of the quantum Galilei group ${\mathcal{F}}_q(G)$ and its Hopf dual ${\mathcal{U}}_q(\mathfrak{g})$. We classify the primitive ideals and simple modules of ${\mathcal{F}}_q(G)$ and ${\mathcal{U}}_q(\mathfrak{g})$ over an algebraically closed field of arbitrary characteristic. We determine their groups of automorphisms over a field of characteristic zero.

Keywords:

• Automorphism group
• primitive ideal
• quantum Galilei group
• simple module

2020 Mathematics Subject Classification:

• 16D60
• 16T20
• 16W20
• 81R50

Data availability statement

Data sharing not applicable to this article as no data sets were generated or analyzed during the current study.

Additional information

Funding

This research was partially supported by the NSFC Grant 11701190.