dorsal/arxiv
View SchemaClassification of the GL(3) Quantum Matrix Groups
| Authors | Holger Ewen, Oleg Ogievetsky |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9412009 |
| URL | https://arxiv.org/abs/q-alg/9412009 |
Abstract
We define quantum matrix groups GL(3) by their coaction on appropriate quantum planes and the requirement that the Poincare series coincides with the classical one. It is shown that this implies the existence of a Yang-Baxter operator. Exploiting stronger equations arising at degree four of the algebra, we classify all quantum matrix groups GL(3). We find 26 classes of solutions, two of which do not admit a normal ordering. The corresponding R-matrices are given.
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"abstract": "We define quantum matrix groups GL(3) by their coaction on appropriate\nquantum planes and the requirement that the Poincare series coincides with the\nclassical one. It is shown that this implies the existence of a Yang-Baxter\noperator. Exploiting stronger equations arising at degree four of the algebra,\nwe classify all quantum matrix groups GL(3). We find 26 classes of solutions,\ntwo of which do not admit a normal ordering. The corresponding R-matrices are\ngiven.",
"arxiv_id": "q-alg/9412009",
"authors": [
"Holger Ewen",
"Oleg Ogievetsky"
],
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"q-alg",
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"title": "Classification of the GL(3) Quantum Matrix Groups",
"url": "https://arxiv.org/abs/q-alg/9412009"
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