The Azumaya locus of certain quantum symplectic spaces

Abstract

In this article, we explore the uniparameter variant of quantum symplectic space. We provide a comprehensive analysis of all potential maximal-dimensional simple modules associated with this algebra. Additionally, we compute the Azumaya locus at odd roots of unity.

2020 MATHEMATICS SUBJECT CLASSIFICATION:

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

KEYWORDS:

• Azumaya locus
• maximal dimensional modules
• polynomial identity algebra
• quantum algebra
• quantum symplectic algebra
• simple modules

Acknowledgments

The author will like to thank National Board of Higher Mathematics, Department of Atomic Energy, Government of India for funding his research. The author extends gratitude to the anonymous referees for their meticulous review of the paper and their invaluable suggestions aimed at enhancing the paper’s quality.

Disclosure statement

The author has received funding from National Board of Higher Mathematics, Department of Atomic Energy, Government of India. The author has no other interests to disclose.

Data availability statement

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