Abstract
In this chapter we show that (9,(G) also falls into the PI Hopf triple pattern. This time, the Hopf centre Z0 is a copy of the classical coordinate ring (9(G), Theorem 1II.7.2. The finite dimensional representation theory of O E (G) is much better understood than that of U E (g), in part because the Poisson geometry of 0(G) is easier than the corresponding geometry for U E (g), (which, as we saw in the last chapter, essentially hinges on the conjugacy classes of G), and in part because the irreducible representations of (9,(G) are all of dimension 1, so that (III.4.11) can be applied. We explain the geometric aspects in (III.7.8), and discuss the irreducible 0, (G)-modulesin (III.7.7) and (II1.7.9).
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© 2002 Springer Basel AG
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Brown, K.A., Goodearl, K.R. (2002). Structure and Representations of O ∈ (G). In: Lectures on Algebraic Quantum Groups. Advanced Courses in Mathematics CRM Barcelona. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8205-7_33
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DOI: https://doi.org/10.1007/978-3-0348-8205-7_33
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-6714-5
Online ISBN: 978-3-0348-8205-7
eBook Packages: Springer Book Archive