dorsal/arxiv
View SchemaClassification of Bicovariant Differential Calculi
| Authors | S. Majid |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9608016 |
| URL | https://arxiv.org/abs/q-alg/9608016 |
Abstract
We show that the bicovariant first order differential calculi on a factorisable semisimple quantum group are in 1-1 correspondence with irreducible representations $V$ of the quantum group enveloping algebra. The corresponding calculus is constructed and has dimension $dim V^2$. The differential calculi on a finite group algebra $C G$ are also classified and shown to be in correspondence with pairs consisting of an irreducible representation $V$ and a continuous parameter in $C P^{dim V -1}$. They have dimension $dim V$. For a classical Lie group we obtain an infinite family of non-standard calculi. General constructions for bicovariant calculi and their quantum tangent spaces are also obtained.
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"abstract": "We show that the bicovariant first order differential calculi on a\nfactorisable semisimple quantum group are in 1-1 correspondence with\nirreducible representations $V$ of the quantum group enveloping algebra. The\ncorresponding calculus is constructed and has dimension $dim V^2$. The\ndifferential calculi on a finite group algebra $C G$ are also classified and\nshown to be in correspondence with pairs consisting of an irreducible\nrepresentation $V$ and a continuous parameter in $C P^{dim V -1}$. They have\ndimension $dim V$. For a classical Lie group we obtain an infinite family of\nnon-standard calculi. General constructions for bicovariant calculi and their\nquantum tangent spaces are also obtained.",
"arxiv_id": "q-alg/9608016",
"authors": [
"S. Majid"
],
"categories": [
"q-alg",
"math.QA"
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"title": "Classification of Bicovariant Differential Calculi",
"url": "https://arxiv.org/abs/q-alg/9608016"
},
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