dorsal/arxiv
View SchemaLeft-Covariant Differential Calculi on SL_q(2) and SL_q(3)
| Authors | Konrad Schm"udgen, Axel Sch"uler |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9601020 |
| URL | https://arxiv.org/abs/q-alg/9601020 |
Abstract
We study $N^2-1$ dimensional left-covariant differential calculi on the quantum group $SL_q(N)$ for which the generators of the quantum Lie algebras annihilate the quantum trace. In this way we obtain one distinguished calculus on $SL_q(2)$ (which corresponds to Woronowicz' 3D-calculus on $SU_q(2)$) and two distinguished calculi on $SL_q(3)$ such that the higher order calculi give the ordinary differential calculus on $SL(2)$ and $SL(3)$, respectively, in the limit $q\rightarrow 1$. Two new differential calculi on $SL_q(3)$ are introduced and developed in detail.
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"abstract": "We study $N^2-1$ dimensional left-covariant differential calculi on the\nquantum group $SL_q(N)$ for which the generators of the quantum Lie algebras\nannihilate the quantum trace. In this way we obtain one distinguished calculus\non $SL_q(2)$ (which corresponds to Woronowicz\u0027 3D-calculus on $SU_q(2)$) and\ntwo distinguished calculi on $SL_q(3)$ such that the higher order calculi give\nthe ordinary differential calculus on $SL(2)$ and $SL(3)$, respectively, in the\nlimit $q\\rightarrow 1$. Two new differential calculi on $SL_q(3)$ are\nintroduced and developed in detail.",
"arxiv_id": "q-alg/9601020",
"authors": [
"Konrad Schm\"udgen",
"Axel Sch\"uler"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Left-Covariant Differential Calculi on SL_q(2) and SL_q(3)",
"url": "https://arxiv.org/abs/q-alg/9601020"
},
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