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Row Reducing Quantum Matrices, the Quantum Determinant, and the Dieudonné Determinant

✍ Scribed by Horia C. Pop

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
285 KB
Volume
193
Category
Article
ISSN
0021-8693

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✦ Synopsis

We prove that row reducing a quantum matrix yields another quantum matrix for the same parameter q. This means that the elements of the new matrix satisfy Ž . the same relations as those of the original quantum matrix ring M n . As a q corollary, we can prove that the image of the quantum determinant in the Ž . abelianization of the total ring of quotients of M n is equal to the Dieudonne q determinant of the quantum matrix. A similar result is proved for the multiparameter quantum determinant.

ᮊ 1997 Academic Press q Ž . domain and it has a total ring of left and right quotients D. We show in 318

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