Algebraic structure of multi-parameter quantum groups

Abstract

Multi-parameter versions U_p(g) and C_p[G] of the standard quantum groups U_q(g) and C_q[G] are considered where G is a semi-simple connected complex algebraic group and g is the Lie algebra of G. The primitive spectrum of C_p[G] is calculated, generalizing a result of Joseph for the standard quantum groups. This classification is compared with the classification of symplectic leaves for the associated Poisson structure on G.

AMS Latex, 37 pages, June 1994; to appear in Advances in Math

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• Quantized primitive ideal spaces as quotients of affine algebraic varieties
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• A class of quadratic matrix algebras arising from the quantized enveloping algebra ${\s U}_q(A_{2n-1})$
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• Prime Ideals of q-Commutative Power Series Rings