Double quantum groups and Iwasawa decomposition

Details Double quantum groups and Iwasawa decomposition Double quantum groups and Iwasawa decomposition

1996-01-23

arxiv.org/abs/q-alg/9601024v1

Mathematics

Quantum Algebra

AMS-Latex, 17 pages

Scientific paper

The double quantum groups are the Hopf algebras underlying the complex quantum groups of which the simplest example is the quantum Lorentz group. They are non- standard quantizations of the double group $G \times G$. We construct a corresponding quantized universal enveloping algebra (QUE) and prove that the pairing between a quantum double group and its QUE is nondegenerate. We analyze the representation theory of these double quantum groups, give a detailed version of the Iwasawa decomposition proved by Podles and Woronowicz for the quantum Lorentz group, and show that they are noetherian algebras. Finally we outline a construction of more general non-standard quantum groups using quantum double groups and their generalizations.

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