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Quantized Rank R Matrices

✍ Scribed by Hans Plesner Jakobsen; Søren Jøndrup

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
424 KB
Volume
246
Category
Article
ISSN
0021-8693

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✦ Synopsis

First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized n = r matrices as well as certain quantized rq 1 Ž . Ž . rq 1 Ž . factor algebras M n of M n are analyzed. For r s 1, . . . , n y 1, M n is q q q the quantized function algebra of rank r matrices obtained by working modulo the Ž . Ž . ideal generated by all r q 1 = r q 1 quantum subdeterminants and a certain localization of this algebra is proved to be isomorphic to a more manageable one. In almost all cases, the quantum parameter is a primitive mth root 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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