dorsal/arxiv
View SchemaDiagonal Crossed Products by Duals of Quasi-Quantum Groups
| Authors | Frank Hausser, Florian Nill |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9708004 |
| URL | https://arxiv.org/abs/q-alg/9708004 |
Abstract
Let \G be a (weak) quasi-Hopf algebra. Using a two-sided \G-coaction on an algebra \M, we construct what we call the diagonal crossed product as a new associative algebra structure on \M\otimes \dG, where \dG is the dual of \G. This construction is largely motivated by the special case \M = \G, for which we obtain an explicit definition of the quantum double \D(\G) for quasi-Hopf algebras. Applications of our formalism include the field algebra construction of Mack and Schomerus as well as the formulation of Hopf Spin chains or lattice current algebras based on truncated quantum groups at roots of unity. A complete proof that \D(\G) is even a (weak) quasi-triangular quasi-Hopf algebra will be given in a separate paper.
{
"annotation_id": "7eabc9cc-0b17-419b-887f-92c33c407b4e",
"date_created": "2026-03-02T18:01:28.701000Z",
"date_modified": "2026-03-02T18:01:28.701000Z",
"file_hash": "acd58f21fa087c5599ac8aaf11106f7f1225d3e1238e79354299acd6c810a6e7",
"private": false,
"record": {
"abstract": "Let \\G be a (weak) quasi-Hopf algebra. Using a two-sided \\G-coaction on an\nalgebra \\M, we construct what we call the diagonal crossed product as a new\nassociative algebra structure on \\M\\otimes \\dG, where \\dG is the dual of \\G.\nThis construction is largely motivated by the special case \\M = \\G, for which\nwe obtain an explicit definition of the quantum double \\D(\\G) for quasi-Hopf\nalgebras. Applications of our formalism include the field algebra construction\nof Mack and Schomerus as well as the formulation of Hopf Spin chains or lattice\ncurrent algebras based on truncated quantum groups at roots of unity. A\ncomplete proof that \\D(\\G) is even a (weak) quasi-triangular quasi-Hopf algebra\nwill be given in a separate paper.",
"arxiv_id": "q-alg/9708004",
"authors": [
"Frank Hausser",
"Florian Nill"
],
"categories": [
"q-alg",
"hep-lat",
"math.QA"
],
"title": "Diagonal Crossed Products by Duals of Quasi-Quantum Groups",
"url": "https://arxiv.org/abs/q-alg/9708004"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "1735fa4d-d90d-440f-a466-cd303bf2cfdf",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}