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Quantized rank R matrices

Hans Plesner Jakobsen·Søren Jøndrup
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Abstract

First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function algebra of rank $r$ matrices obtained by working modulo the ideal generated by all $(r+1)\times (r+1)$ quantum subdeterminants and a certain localization of this algebra is proved to be isomorphic to a more manageable one. In all cases, the quantum parameter is a primitive $m$th roots of unity. The degrees and centers of the algebras are determined when $m$ is a prime and the general structure is obtained for arbitrary $m$.

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Hans Plesner Jakobsen, Søren Jøndrup. 2001-05-23. Quantized rank R matrices. https://arxiv.org/abs/math/9902133

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