English

Monomial bialgebras

Quantum Algebra 2026-02-10 v2 Mathematical Physics Combinatorics math.MP Representation Theory

Abstract

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.

Keywords

Cite

@article{arxiv.2602.02342,
  title  = {Monomial bialgebras},
  author = {Arkady Berenstein and Jacob Greenstein and Jian-Rong Li},
  journal= {arXiv preprint arXiv:2602.02342},
  year   = {2026}
}

Comments

75 pages; references added, some arguments streamlined, misprints corrected