dorsal/arxiv
View SchemaMatched differential calculus on the quantum groups $GL_q(2,C),SL_q(2,C),C_q(2|0)$
| Authors | V. P. Akulov, V. D. Gershun |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9509030 |
| URL | https://arxiv.org/abs/q-alg/9509030 |
Abstract
We proposed the construction of the differential calculus on the quantum group and its subgroup with the property of the natural reduction: the differential calculus on the quantum group $GL_q(2,C)$ has to contain the differential calculus on the quantum subgroup $SL_q(2,C)$ and quantum plane $C_q(2|0)$ (''quantum matrjoshka''). We found, that there are two differential calculi, associated to the left differential Maurer--Cartan 1-forms and to the right differential 1-forms. Matched reduction take the degeneracy between the left and right differentials. The classical limit ($q\to 1$) of the ''left'' differential calculus and of the ''right'' differential calculus is undeformed differential calculus. The condition ${\cal D}_qG=1$ gives the differential calculus on $SL_q(2,C)$, which contains the differential calculus on the quantum plane $C_q(2|0)$.
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"abstract": "We proposed the construction of the differential calculus on the quantum\ngroup and its subgroup with the property of the natural reduction: the\ndifferential calculus on the quantum group $GL_q(2,C)$ has to contain the\ndifferential calculus on the quantum subgroup $SL_q(2,C)$ and quantum plane\n$C_q(2|0)$ (\u0027\u0027quantum matrjoshka\u0027\u0027). We found, that there are two differential\ncalculi, associated to the left differential Maurer--Cartan 1-forms and to the\nright differential 1-forms. Matched reduction take the degeneracy between the\nleft and right differentials. The classical limit ($q\\to 1$) of the \u0027\u0027left\u0027\u0027\ndifferential calculus and of the \u0027\u0027right\u0027\u0027 differential calculus is undeformed\ndifferential calculus. The condition ${\\cal D}_qG=1$ gives the differential\ncalculus on $SL_q(2,C)$, which contains the differential calculus on the\nquantum plane $C_q(2|0)$.",
"arxiv_id": "q-alg/9509030",
"authors": [
"V. P. Akulov",
"V. D. Gershun"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Matched differential calculus on the quantum groups $GL_q(2,C),SL_q(2,C),C_q(2|0)$",
"url": "https://arxiv.org/abs/q-alg/9509030"
},
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