dorsal/arxiv
View SchemaFinite Group Factorisations and Braiding
| Authors | E. Beggs, J. Gould, S. Majid |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9503018 |
| URL | https://arxiv.org/abs/q-alg/9503018 |
Abstract
We compute the quantum double, braiding and other canonical Hopf algebra constructions for the bicrossproduct Hopf algebra $H$ associated to the factorization of a finite group into two subgroups. The representations of the quantum double are described by a notion of bicrossed bimodules, generalising the cross modules of Whitehead. We also show that self-duality structures for the bicrossproduct Hopf algebras are in one-one correspondence with factor-reversing group isomorphisms. The example $Z_6Z_6$ is given in detail. We show further that the quantum double $D(H)$ is the twisting of $D(X)$ by a non-trivial quantum cocycle, where $X$ is the associated double cross product group.
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"abstract": "We compute the quantum double, braiding and other canonical Hopf algebra\nconstructions for the bicrossproduct Hopf algebra $H$ associated to the\nfactorization of a finite group into two subgroups. The representations of the\nquantum double are described by a notion of bicrossed bimodules, generalising\nthe cross modules of Whitehead. We also show that self-duality structures for\nthe bicrossproduct Hopf algebras are in one-one correspondence with\nfactor-reversing group isomorphisms. The example $Z_6Z_6$ is given in detail.\n We show further that the quantum double $D(H)$ is the twisting of $D(X)$ by a\nnon-trivial quantum cocycle, where $X$ is the associated double cross product\ngroup.",
"arxiv_id": "q-alg/9503018",
"authors": [
"E. Beggs",
"J. Gould",
"S. Majid"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Finite Group Factorisations and Braiding",
"url": "https://arxiv.org/abs/q-alg/9503018"
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