dorsal/arxiv
View SchemaA Coassociative C*-Quantum Group with Non-Integral Dimensions
| Authors | G. Bohm, K. Szlachanyi |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9509008 |
| URL | https://arxiv.org/abs/q-alg/9509008 |
| DOI | 10.1007/BF01815526 |
Abstract
By weakening the counit and antipode axioms of a C*-Hopf algebra and allowing for the coassociative coproduct to be non-unital we obtain a quantum group, that we call a weak C*-Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. This amounts to generalizing the Baaj-Skandalis multiplicative unitaries to multipicative partial isometries. Every weak C*-Hopf algebra has a dual which is again a weak C*-Hopf algebra. An explicit example is presented with Lee-Yang fusion rules. We shortly discuss applications to amalgamated crossed products, doubles, and quantum chains.
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"abstract": "By weakening the counit and antipode axioms of a C*-Hopf algebra and allowing\nfor the coassociative coproduct to be non-unital we obtain a quantum group,\nthat we call a weak C*-Hopf algebra, which is sufficiently general to describe\nthe symmetries of essentially arbitrary fusion rules. This amounts to\ngeneralizing the Baaj-Skandalis multiplicative unitaries to multipicative\npartial isometries. Every weak C*-Hopf algebra has a dual which is again a weak\nC*-Hopf algebra. An explicit example is presented with Lee-Yang fusion rules.\nWe shortly discuss applications to amalgamated crossed products, doubles, and\nquantum chains.",
"arxiv_id": "q-alg/9509008",
"authors": [
"G. Bohm",
"K. Szlachanyi"
],
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],
"doi": "10.1007/BF01815526",
"title": "A Coassociative C*-Quantum Group with Non-Integral Dimensions",
"url": "https://arxiv.org/abs/q-alg/9509008"
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