The Center of the Dipper Donkin Quantized Matrix Algebra

We compute the center in case q is a primitive root of unity. 1. Introduction Let F be a eld of characteristic zero. There are several ways to quantize the matrix algebra M n (F). Among them, the most common is probably the algebra introduced by Faddeev, Reshetikhin, and Takhtajan in 4]. Denote that algebra by M n (q). In 3] Dipper and Donkin deened another quantized matrix algebra which has many features which are diierent from M n (q) e.g. the quantized determinant is not central. In 9] a two parameter quantized matrix algebra was deened for which the above two quantized matrix algebras are special cases. Even more general multi-parameters quantized algebras have been introduced by Artin, Schelter, and Tate 1], Sudbery 8], and Reshitikhin 7], independently. To understand the structure of these quantized matrix algebras it is natural to determine their centers. In 6] the center of M n (q) was determined by nding the degree of the algebra over its center and by investigating certain quantized minors. In this paper we compute the center of the quantized matrix algebra constructed by Dipper and Donkin 3] by similar methods. Throughout, the quantum parameter is