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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.02342 |
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| _version_ | 1866914313520807936 |
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| author | Berenstein, Arkady Greenstein, Jacob Li, Jian-Rong |
| author_facet | Berenstein, Arkady Greenstein, Jacob Li, Jian-Rong |
| contents | Starting from a single solution of QYBE (or CYBE) we produce an infinite family of solutions of QYBE (or CYBE) parametrized by transitive arrays and, in particular, by signed permutations. We are especially interested in cases when such solutions yield quasi-triangular structures on direct powers of Lie bialgebras and tensor powers of Hopf algebras. We obtain infinite families of such structures as well and study the corresponding Poisson-Lie structures and co-quasi-triangular algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02342 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monomial bialgebras Berenstein, Arkady Greenstein, Jacob Li, Jian-Rong Quantum Algebra Mathematical Physics Combinatorics Representation Theory 16T10, 16T25, 17B37, 17B62, 17B63, 20G42 Starting from a single solution of QYBE (or CYBE) we produce an infinite family of solutions of QYBE (or CYBE) parametrized by transitive arrays and, in particular, by signed permutations. We are especially interested in cases when such solutions yield quasi-triangular structures on direct powers of Lie bialgebras and tensor powers of Hopf algebras. We obtain infinite families of such structures as well and study the corresponding Poisson-Lie structures and co-quasi-triangular algebras. |
| title | Monomial bialgebras |
| topic | Quantum Algebra Mathematical Physics Combinatorics Representation Theory 16T10, 16T25, 17B37, 17B62, 17B63, 20G42 |
| url | https://arxiv.org/abs/2602.02342 |