论文标题
正式的多参数量子组，变形和专业
Formal multiparameter quantum groups, deformations and specializations
论文作者
论文摘要
我们介绍了形式的多组量子量子通用代数的概念 - 简短的绒毛 - 作为Drinfeld的量子群的直接概括。然后，我们表明，绒毛的类别在变形下通过（“ toral”）曲折和（“ toral”）2 cocycles的变形闭合：因此，所有“多参数正式Quea”到目前为止都被恢复，因为落在此类中。特别是，我们证明，任何绒毛与特林菲尔德的标准Quea的合适变形，扭曲或2循环相同。 我们还介绍了多参数lie bialgebras（简而言之，MPLBA），并通过扭曲和2个循环来考虑它们的变形。每个绒毛的半经典极限是合适的MPLBA，相反，每个MPLBA都可以量化为合适的绒毛。最后，我们证明，大致说明“专业化”的两个过程（fompquea of mplba）和“变形（通过toral twist或toral 2 cocycle）” - 在绒毛或mplba的水平上 - 彼此之间的通勤。
We introduce the notion of formal multiparameter quantum universal enveloping algebras - in short FoMpQUEA - as a straightforward generalization of Drinfeld's quantum group. Then we show that the class of FoMpQUEA's is closed under deformations by ("toral") twists and deformations by ("toral") 2-cocycles: as a consequence, all "multiparameter formal QUEA's" considered so far are recovered, as falling within this class. In particular, we prove that any FoMpQUEA is isomorphic to a suitable deformation, by twist or by 2-cocycle, of Drinfeld's standard QUEA. We introduce also multiparameter Lie bialgebras (in short, MpLbA's), and we consider their deformations, by twist and by 2-cocycles. The semiclassical limit of every FoMpQUEA is a suitable MpLbA, and conversely each MpLbA can be quantized to a suitable FoMpQUEA. In the end, we prove that, roughly speaking, the two processes of "specialization" (of FoMpQUEA to a MpLbA) and of "deformation (by toral twist or toral 2-cocycle)" - at the level of FoMpQUEA's or of MpLbA's - do commute with each other.
