dorsal/arxiv
View SchemaQuasitriangular and differential structures on bicrossproduct Hopf algebras
| Authors | E. Beggs, S. Majid |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9701041 |
| URL | https://arxiv.org/abs/q-alg/9701041 |
Abstract
Let X=GM be a finite group factorisation. It is shown that the quantum double D(H) of the associated bicrossproduct Hopf algebra $H=kM\cobicross k(G)$ is itself a bicrossproduct $kX\cobicross k(Y)$ associated to a group YX, where $Y=G\times M^{op}$. This provides a class of bicrossproduct Hopf algebras which are quasitriangular. We also construct a subgroup $Y^\theta X^\theta$ associated to every order-reversing automorphism $\theta$ of X. The corresponding Hopf algebra $kX^\theta\cobicross k(Y^\theta)$ has the same coalgebra as H. Using related results, we classify the first order bicovariant differential calculi on H in terms of orbits in a certain quotient space of X.
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"date_created": "2026-03-02T18:01:27.680000Z",
"date_modified": "2026-03-02T18:01:27.680000Z",
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"abstract": "Let X=GM be a finite group factorisation. It is shown that the quantum double\nD(H) of the associated bicrossproduct Hopf algebra $H=kM\\cobicross k(G)$ is\nitself a bicrossproduct $kX\\cobicross k(Y)$ associated to a group YX, where\n$Y=G\\times M^{op}$. This provides a class of bicrossproduct Hopf algebras which\nare quasitriangular. We also construct a subgroup $Y^\\theta X^\\theta$\nassociated to every order-reversing automorphism $\\theta$ of X. The\ncorresponding Hopf algebra $kX^\\theta\\cobicross k(Y^\\theta)$ has the same\ncoalgebra as H. Using related results, we classify the first order bicovariant\ndifferential calculi on H in terms of orbits in a certain quotient space of X.",
"arxiv_id": "q-alg/9701041",
"authors": [
"E. Beggs",
"S. Majid"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Quasitriangular and differential structures on bicrossproduct Hopf algebras",
"url": "https://arxiv.org/abs/q-alg/9701041"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "c202e11a-be4b-4bed-9d86-bb453b230260",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
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