Quasi-quantum groups arising from cotensor coquasi-Hopf algebras
Abstract
In this paper, we show that for any coquasi-Hopf algebra H and any H-Majid bimodule M, the cotensor coalgebra CoTH(M) admits a graded coquasi-Hopf algebra structure. We then define the standard filtration of a coquasi-Hopf algebra and show that the associated graded coquasi-Hopf algebra admits an embedding into a cotensor coquasi-Hopf algebra that preserves degrees zero and one. If, in addition, this coquasi-Hopf algebra is coquasitriangular (respectively, coribbon), then the cotensor coquasi-Hopf algebra is also coquasitriangular (respectively, coribbon), and the above embedding is a morphism of coquasitriangular (respectively, coribbon) coquasi-Hopf algebras. As a byproduct, we prove that the coquasi-antipode of a coquasi-Hopf algebra with the dual Chevalley property is bijective. Moreover, we establish graded quasi-coquasi-Hopf pairings between tensor quasi-Hopf algebras and cotensor coquasi-Hopf algebras.
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BibTeX
@misc{yu2026quasiquantum,
title = {{Quasi-quantum groups arising from cotensor coquasi-Hopf algebras}},
author = {Jing Yu and Xiangjun Zhen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08361},
eprint = {2610.08361},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08361},
}
RIS
TY - UNPB
TI - Quasi-quantum groups arising from cotensor coquasi-Hopf algebras
AU - Jing Yu
AU - Xiangjun Zhen
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.08361
UR - https://arxiv.org/abs/2610.08361
AB - In this paper, we show that for any coquasi-Hopf algebra H and any H-Majid bimodule M, the cotensor coalgebra CoT_H(M) admits a graded coquasi-Hopf algebra structure. We then define the standard filtration of a coquasi-Hopf algebra and show that the associated graded coquasi-Hopf algebra admits an embedding into a cotensor coquasi-Hopf algebra that preserves degrees zero and one. If, in addition, this coquasi-Hopf algebra is coquasitriangular (respectively, coribbon), then the cotensor coquasi-Hopf algebra is also coquasitriangular (respectively, coribbon), and the above embedding is a morphism of coquasitriangular (respectively, coribbon) coquasi-Hopf algebras. As a byproduct, we prove that the coquasi-antipode of a coquasi-Hopf algebra with the dual Chevalley property is bijective. Moreover, we establish graded quasi-coquasi-Hopf pairings between tensor quasi-Hopf algebras and cotensor coquasi-Hopf algebras.
ER -