Abstract
Quantized coordinate rings have been constructed for all connected, complex, semisimple algebraic groups G. We describe here the generic case, that is, the single-parameter quantized coordinate rings (7 q (G) with q not a root of unity; the root of unity case will be discussed in Chapter III.7. As with quantized enveloping algebras, G is just a suggestive label, and quantized coordinate rings for G can be defined over (almost) arbitrary fields. Since 0 q (G) is built from coordinate functions of certain representations of the quantized enveloping algebra of its Lie algebra, we rely heavily on the results of the previous chapter. Throughout the chapter, q denotes a fixed nonzero scalar, which is not a root of unity, in our base field k. KeywordsHopf AlgebraCoordinate FunctionCoordinate RingSemisimple GroupHigh Weight ModuleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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