Geodesic
Division rings of quotients and central elements of multiparameter quantizations
Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 835-855 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that the algebra of regular functions on quantum $m\times n$ matrices admits a division ring of quotients and that this division ring is a division ring of twisted rational functions. A description is given of the field of central elements in the division ring of rational functions on quantum $m\times n$ matrices in the one-parameter and multiparameter cases. In the one-parameter case for $q$ of a general form the center is a purely transcendental extension of a field $\mathbb K$ of degree $l$ (were $l$ is the greatest common divisor of $m$ and $n$) if both numbers $m/l$ and $n/l$ are odd. If at least one of the numbers $m/l$ and $n/l$ is even, then the center is scalar. In the multiparameter case the answer depends upon the parameters $P$,$Q$, $c$. Here the generators of the center are described and it is proved that the center is scalar for the case of even $n$ and parameters of a general form. Analogous result are obtained for the division ring of rational functions on a quantum Borel subgroup of $GL_{P,Q,c}(n)$. 
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     author = {V. G. Mosin and A. N. Panov},
     title = {Division rings of quotients and central elements of multiparameter quantizations},
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     year = {1996},
     volume = {187},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_6_a3/}
}
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V. G. Mosin; A. N. Panov. Division rings of quotients and central elements of multiparameter quantizations. Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 835-855. http://geodesic.mathdoc.fr/item/SM_1996_187_6_a3/

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