Azumaya Loci Of The Quantum Euclidean $2n$-Space

TL;DR

This paper investigates the Azumaya loci of quantum Euclidean 2n-space, identifying and characterizing maximal-dimensional simple modules through center computation and establishing their correspondence.

Contribution

It introduces a new class of maximal-dimensional simple modules and proves they exhaust all such modules for the algebra.

Findings

Identified the Azumaya locus of the quantum Euclidean 2n-space.

Constructed a significant class of maximal-dimensional simple modules.

Proved these modules are exactly all maximal-dimensional simple modules.

Abstract

This article delves into the Azumaya loci of quantum euclidean 2n-space, providing a comprehensive exploration. We introduce a significant class of maximal-dimensional simple modules associated with this algebra. Moreover, we establish a proof asserting that the maximal-dimensional simple modules are exactly the ones we have constructed. The computation of the algebra's center, coupled with the necessary and sufficient conditions derived for maximal-dimensional simple modules, enables us to determine the Azumaya locus of the algebra.