On the \(q\)-commutations in \(U_q({\mathfrak n})\) at roots of one
Let \({\mathfrak g}\) be a semisimple Lie algebra with triangular decomposition \({\mathfrak g}= {\mathfrak n} + {\mathfrak h} + {\mathfrak n} ^{-}\), and let \(\varepsilon\) be a root of unity. Let \(U ^{+} _{\varepsilon}\) (resp. \(U ^{\text{res} +} _{\varepsilon}\)) be the nonrestricted (resp. restricted) quantum enveloping algebra of \({\mathfrak n}\). In the paper under review the author proves that {Fract} \(U ^{+} _{\varepsilon}\) is a quantum Weyl field and gives a description of the \(\varepsilon\)-center of \(U ^{+} _{\varepsilon}\). Let \(U_{\varepsilon} ^{\text{fin} +}\) be the finite part of \(U_{\varepsilon} ^{\text{res} +}\). It is proved that the \(U_{\varepsilon} ^{\text{fin} +}\)-coinvariant space of a Weyl module is \(\varepsilon\)-central.
scientific article; zbMATH DE number 1251409