dorsal/arxiv
View SchemaDouble quantum groups and Iwasawa decomposition
| Authors | Timothy J. Hodges |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9601024 |
| URL | https://arxiv.org/abs/q-alg/9601024 |
Abstract
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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"abstract": "The double quantum groups are the Hopf algebras underlying the complex\nquantum groups of which the simplest example is the quantum Lorentz group. They\nare non- standard quantizations of the double group $G \\times G$. We construct\na corresponding quantized universal enveloping algebra (QUE) and prove that the\npairing between a quantum double group and its QUE is nondegenerate. We analyze\nthe representation theory of these double quantum groups, give a detailed\nversion of the Iwasawa decomposition proved by Podles and Woronowicz for the\nquantum Lorentz group, and show that they are noetherian algebras. Finally we\noutline a construction of more general non-standard quantum groups using\nquantum double groups and their generalizations.",
"arxiv_id": "q-alg/9601024",
"authors": [
"Timothy J. Hodges"
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"title": "Double quantum groups and Iwasawa decomposition",
"url": "https://arxiv.org/abs/q-alg/9601024"
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