English

The PBW theorem for the affine Yangians

Representation Theory 2018-04-13 v1 Quantum Algebra

Abstract

We prove that the Yangian associated to an untwisted symmetric affine Kac-Moody Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter is constructed by the authors in arXiv:1407.7994 as an algebraic formalism of the cohomological Hall algebras. As a consequence, we obtain the Poincare-Birkhoff-Witt (PBW) theorem for this class of affine Yangians. Another independent proof of the PBW theorem is given recently by Guay-Regelskis-Wendlandt.

Keywords

Cite

@article{arxiv.1804.04375,
  title  = {The PBW theorem for the affine Yangians},
  author = {Yaping Yang and Gufang Zhao},
  journal= {arXiv preprint arXiv:1804.04375},
  year   = {2018}
}

Comments

12 pages, preliminary version, comments welcome

R2 v1 2026-06-23T01:21:24.481Z