dorsal/arxiv
View SchemaClassification of the quantum deformation of the superalgebra $GL(1|1)$
| Authors | L. Frappat, V. Hussin, G. Rideau |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9705024 |
| URL | https://arxiv.org/abs/q-alg/9705024 |
| DOI | 10.1088/0305-4470/31/17/014 |
Abstract
We present a classification of the possible quantum deformations of the supergroup $GL(1|1)$ and its Lie superalgebra $gl(1|1)$. In each case, the (super)commutation relations and the Hopf structures are explicitly computed. For each $R$ matrix, one finds two inequivalent coproducts whether one chooses an unbraided or a braided framework while the corresponding structures are isomorphic as algebras. In the braided case, one recovers the classical algebra $gl(1|1)$ for suitable limits of the deformation parameters but this is no longer true in the unbraided case.
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"abstract": "We present a classification of the possible quantum deformations of the\nsupergroup $GL(1|1)$ and its Lie superalgebra $gl(1|1)$. In each case, the\n(super)commutation relations and the Hopf structures are explicitly computed.\nFor each $R$ matrix, one finds two inequivalent coproducts whether one chooses\nan unbraided or a braided framework while the corresponding structures are\nisomorphic as algebras. In the braided case, one recovers the classical algebra\n$gl(1|1)$ for suitable limits of the deformation parameters but this is no\nlonger true in the unbraided case.",
"arxiv_id": "q-alg/9705024",
"authors": [
"L. Frappat",
"V. Hussin",
"G. Rideau"
],
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"q-alg",
"math.QA"
],
"doi": "10.1088/0305-4470/31/17/014",
"title": "Classification of the quantum deformation of the superalgebra $GL(1|1)$",
"url": "https://arxiv.org/abs/q-alg/9705024"
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