Row reducing quantum matrices, the quantum determinant, and the Dieudonne determinant

[摘要] 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 the same relations as those of the original quantum matrix ring M-q(n). As a corollary, we can prove that the image of the quantum determinant in the abelianization of the total ring of quotients of M-q(n) is equal to the Dieudonne determinant of the quantum matrix. A similar result is proved for the multiparameter quantum determinant. (C) 1997 Academic Press.

[发布日期] 1997-07-01