dorsal/arxiv
View SchemaTopics in hidden symmetries. IV
| Authors | Denis V. Juriev |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9611019 |
| URL | https://arxiv.org/abs/q-alg/9611019 |
Abstract
This note being devoted to some aspects of the inverse problem of representation theory explicates the links between researches on the Sklyanin algebras and the author's (based on the noncommutative geometry) approach to the setting free of hidden symmetries in terms of "the quantization of constants". Namely, the Racah-Wigner algebra for the Sklyanin algebra is constructed. It may be considered as a result of the quantization of constants in the Racah-Wigner algebra for the Lie algebra $sl(2,C)$. The Racah-Wigner algebra for the Sklyanin algebra is an example of the noncommutative weighted shift operator algebras (NWSO-algebras), which generalize the mho-algebras introduced by the author earlier. If the Sklyanin algebra is interpreted as an algebra of anomalous spins then the Racah-Wigner algebra for it may be regarded as an enlargement of the Sklyanin algebra by operators of the anomalous spin-spin interaction (of tensor type).
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"abstract": "This note being devoted to some aspects of the inverse problem of\nrepresentation theory explicates the links between researches on the Sklyanin\nalgebras and the author\u0027s (based on the noncommutative geometry) approach to\nthe setting free of hidden symmetries in terms of \"the quantization of\nconstants\". Namely, the Racah-Wigner algebra for the Sklyanin algebra is\nconstructed. It may be considered as a result of the quantization of constants\nin the Racah-Wigner algebra for the Lie algebra $sl(2,C)$. The Racah-Wigner\nalgebra for the Sklyanin algebra is an example of the noncommutative weighted\nshift operator algebras (NWSO-algebras), which generalize the mho-algebras\nintroduced by the author earlier. If the Sklyanin algebra is interpreted as an\nalgebra of anomalous spins then the Racah-Wigner algebra for it may be regarded\nas an enlargement of the Sklyanin algebra by operators of the anomalous\nspin-spin interaction (of tensor type).",
"arxiv_id": "q-alg/9611019",
"authors": [
"Denis V. Juriev"
],
"categories": [
"q-alg",
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"title": "Topics in hidden symmetries. IV",
"url": "https://arxiv.org/abs/q-alg/9611019"
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