English

A new new coproduct on quantum loop algebras

Representation Theory 2026-04-07 v2 Quantum Algebra

Abstract

Quantum loop algebras generalize Uq(g^)U_q(\widehat{\mathfrak{g}}) for simple Lie algebras g\mathfrak{g}, and they include examples such as quantum affinizations of Kac-Moody Lie algebras, K-theoretic Hall algebras of quivers, and BPS algebras for toric Calabi-Yau threefolds. In the present paper, we define a coproduct on general quantum loop algebras, which coincides with the Drinfeld-Jimbo coproduct in the particular case of Uq(g^)U_q(\widehat{\mathfrak{g}}) . We investigate the consequences of our construction for the representation theory of quantum loop algebras, particularly for tensor products of modules and R-matrices.

Keywords

Cite

@article{arxiv.2602.01130,
  title  = {A new new coproduct on quantum loop algebras},
  author = {Andrei Neguţ},
  journal= {arXiv preprint arXiv:2602.01130},
  year   = {2026}
}
R2 v1 2026-07-01T09:30:03.675Z