Simple modules over Kq[X,Y]⋊Uq≥0(sl2) and Kq[X,Y]⋊Uq(sl2) at root of unity

Abstract

In this article the smash product algebras as in the title due to V. V. Bavula and T. Lu have been studied at the root of unity. A full classification of simple modules over ${\mathbb{K}}_q[X,Y]⋊U_q^{\ge 0}(\mathfrak{s}{\mathfrak{l}}_2)$ along with a class of finite dimensional indecomposable modules are presented. Also simple X, Y-torsionfree modules over ${\mathbb{K}}_q[X,Y]⋊U_q(\mathfrak{s}{\mathfrak{l}}_2)$ are classified.

Keywords:

• Polynomial identity algebra
• quantum algebra
• quantum spatial ageing algebra
• simple module
• torsion module

2020 Mathematics Subject Classification:

• 16D25
• 16D60
• 16D70
• 16S85
• 16T20
• 16R20

Acknowledgments

The authors deeply thank their supervisor Ashish Gupta for setting up the problem, going through the paper and supervising it. They thank the anonymous referees for carefully reading the paper. The authors would also like to thank the National Board of Higher Mathematics, Department of Atomic Energy, India for funding their research.