Classification of twisted Yangians as coideal subalgebras of Yangians
Abstract
Let g be a complex simple Lie algebra with an involution ω. We classify the homogeneous right coideal subalgebras of the Yangian of g whose classical limit is the enveloping algebra of the twisted current algebra, embedded in the standard way, without assuming any formula for the coaction. For nontrivial ω, they form a family parametrized by a spectral parameter and an element of the center of the fixed-point subalgebra; for ω=id, only a spectral parameter occurs. All members of the family are isomorphic as graded algebras, through explicit isomorphisms. In particular, the twisted Yangians with a central correction introduced by Huang and Lu are coideal quantizations, and the imathYangian of quasi-split type A2n is isomorphic to the traditional twisted Yangian studied by MacKay and by Belliard and Regelskis. The PBW property is proved uniformly from the classical affine Serre relations, without quantum defining relations. We also recover finite presentations in split and quasi-split types and verify the technical hypotheses of the quantum duality principle used by Lu, Wang, and Weekes.
Related
- Schur--Weyl duality for coideal subalgebras of quantum affine superalgebras of type A
- One-dimensional partial actions of 8-dimensional Hopf algebras and right coideal subalgebras
- Right Coideal Subalgebras, Hopf Galois Objects, and imath-Hopf Algebras
- Twisted Yangians of split types BI, CI, DI and Drinfeld type current relations
- Classification of finite-dimensional Nichols algebras of rank two in twisted Yetter--Drinfeld categories
BibTeX
@misc{lu2026classification,
title = {{Classification of twisted Yangians as coideal subalgebras of Yangians}},
author = {Kang Lu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25003},
eprint = {2610.25003},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25003},
}
RIS
TY - UNPB
TI - Classification of twisted Yangians as coideal subalgebras of Yangians
AU - Kang Lu
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25003
UR - https://arxiv.org/abs/2610.25003
AB - Let g be a complex simple Lie algebra with an involution ω. We classify the homogeneous right coideal subalgebras of the Yangian of g whose classical limit is the enveloping algebra of the twisted current algebra, embedded in the standard way, without assuming any formula for the coaction. For nontrivial ω, they form a family parametrized by a spectral parameter and an element of the center of the fixed-point subalgebra; for ω=id, only a spectral parameter occurs. All members of the family are isomorphic as graded algebras, through explicit isomorphisms. In particular, the twisted Yangians with a central correction introduced by Huang and Lu are coideal quantizations, and the imathYangian of quasi-split type A_2n is isomorphic to the traditional twisted Yangian studied by MacKay and by Belliard and Regelskis. The PBW property is proved uniformly from the classical affine Serre relations, without quantum defining relations. We also recover finite presentations in split and quasi-split types and verify the technical hypotheses of the quantum duality principle used by Lu, Wang, and Weekes.
ER -