K. Iohara et F. Malikov, RINGS OF SKEW POLYNOMIALS AND GELFAND-KIRILLOV CONJECTURE FOR QUANTUMGROUPS, Communications in Mathematical Physics, 164(2), 1994, pp. 217-237
We introduce and study action of quantum groups on skew polynomial rin
gs and related rings of quotients. This leads to a ''q-deformation'' o
f the Gel'fand-Kirillov conjecture which we partially prove. We propos
e a construction of automorphisms of certain non-commutative rings of
quotients coming from complex powers of quantum group generators; this
is applied to explicit calculation of singular vectors in Verma modul
es over U(q)(sI(n+1)). We finally give a definition of a q-connection
with coefficients in a ring of skew polynomials and study the structur
e of quantum group modules twisted by a q-connection.