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

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.