Abstract
Throughout this chapter we’ll assume that g is a finite dimensional semisimple complex Lie algebra and that e is a primitive £th root of unity in the fieldkof characteristic0,where
P > 3 is odd, and prime to 3 if g contains a factor of type G2. (1)
Our aim in this chapter is to examine how the structure of UE(5(2(k)) which we found in Chapter III.2 generalises to arbitrary semisimple g. We’ll see (111.6.2) that (Mg) is a PI Hopf triple in the language of Chapter 111.4. Moreover the construction of (I11.5.6) can be used to obtain a structure of Poisson group on the Hopf centre Z0 of U E (g), so that the representation theory of U E (g) can be studied with the help of (III.5.8).
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© 2002 Springer Basel AG
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Brown, K.A., Goodearl, K.R. (2002). Structure of U ∈ (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_32
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DOI: https://doi.org/10.1007/978-3-0348-8205-7_32
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-6714-5
Online ISBN: 978-3-0348-8205-7
eBook Packages: Springer Book Archive