dorsal/arxiv
View SchemaThe structure of quantum Lie algebras for the classical series B_l, C_l and D_l
| Authors | Gustav W. Delius, Christopher Gardner, Mark D. Gould |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9706029 |
| URL | https://arxiv.org/abs/q-alg/9706029 |
| DOI | 10.1088/0305-4470/31/8/012 |
| Journal | J. Phys. A: Math. Gen. 31 1995-2019 |
Abstract
The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at $q=1$. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint ---> adjoint. We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B_l, C_l and D_l. In the quantum case also the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.
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"abstract": "The structure constants of quantum Lie algebras depend on a quantum\ndeformation parameter q and they reduce to the classical structure constants of\na Lie algebra at $q=1$. We explain the relationship between the structure\nconstants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for\nadjoint x adjoint ---\u003e adjoint. We present a practical method for the\ndetermination of these quantum Clebsch-Gordan coefficients and are thus able to\ngive explicit expressions for the structure constants of the quantum Lie\nalgebras associated to the classical Lie algebras B_l, C_l and D_l.\n In the quantum case also the structure constants of the Cartan subalgebra are\nnon-zero and we observe that they are determined in terms of the simple quantum\nroots. We introduce an invariant Killing form on the quantum Lie algebras and\nfind that it takes values which are simple q-deformations of the classical\nones.",
"arxiv_id": "q-alg/9706029",
"authors": [
"Gustav W. Delius",
"Christopher Gardner",
"Mark D. Gould"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1088/0305-4470/31/8/012",
"journal_ref": "J. Phys. A: Math. Gen. 31 1995-2019",
"title": "The structure of quantum Lie algebras for the classical series B_l, C_l and D_l",
"url": "https://arxiv.org/abs/q-alg/9706029"
},
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