dorsal/arxiv
View SchemaHigher Order Differential Calculus on $SL_q(N)$
| Authors | I. Heckenberger, A. Schueler |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9708013 |
| URL | https://arxiv.org/abs/q-alg/9708013 |
| DOI | 10.1023/A:1021614302046 |
Abstract
Let $\Gamma$ be an $N^2$-dimensional bicovariant first order differential calculus on a Hopf algebra $SL_q(N)$. There are three possibilities to construct a differential Z-graded Hopf algebra $\Gamma^\wedge$ which contains $\Gamma$ as its first order part. Let $q$ be a transcendental complex number. For $N>2$ these three Z-graded Hopf algebras coincide. For Woronowicz' external algebra we calculate the dimensions of the spaces of left-invariant and bi-invariant $k$-forms. In this case each bi-invariant form is closed. In case of $4D_\pm$ calculi on $SL_q(2)$ the universal calculus is strictly larger than the other two calculi. In particular, the bi-invariant 1-form is not closed.
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"abstract": "Let $\\Gamma$ be an $N^2$-dimensional bicovariant first order differential\ncalculus on a Hopf algebra $SL_q(N)$. There are three possibilities to\nconstruct a differential Z-graded Hopf algebra $\\Gamma^\\wedge$ which contains\n$\\Gamma$ as its first order part. Let $q$ be a transcendental complex number.\nFor $N\u003e2$ these three Z-graded Hopf algebras coincide. For Woronowicz\u0027 external\nalgebra we calculate the dimensions of the spaces of left-invariant and\nbi-invariant $k$-forms. In this case each bi-invariant form is closed. In case\nof $4D_\\pm$ calculi on $SL_q(2)$ the universal calculus is strictly larger than\nthe other two calculi. In particular, the bi-invariant 1-form is not closed.",
"arxiv_id": "q-alg/9708013",
"authors": [
"I. Heckenberger",
"A. Schueler"
],
"categories": [
"q-alg",
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],
"doi": "10.1023/A:1021614302046",
"title": "Higher Order Differential Calculus on $SL_q(N)$",
"url": "https://arxiv.org/abs/q-alg/9708013"
},
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