Quotients of graded quasi-Hopf algebras

Abstract

We classify the quasi-Hopf ideals of quasi-Hopf algebras faithfully graded by arbitrary groups. Each ideal determines a normal subgroup, recording which degrees are identified in the quotient, together with an invariant ideal in the corresponding neutral component. We refine this description using an ideal of the original neutral component and a retraction of a naturally associated intermediate quotient. We prove that this intermediate quotient splits as the tensor product of its neutral component with the group algebra of the normal subgroup. For fixed subgroup and neutral-component data, the possible ideals, whenever they exist, form a torsor described by equivariant homomorphisms into central group-like elements. Our results require neither finite dimensionality nor bijectivity of the antipode. We apply them to cocentral abelian extensions with possibly infinite grading, finite-dimensional neutral component, and nontrivial reassociator.

Graded Algebras of Modular Forms and Sign Changes of Fourier Coefficients for Eta Quotients
Jianwen Gan
arXiv25 Oct 2026PreprintarXiv licenceFull textAlgebra & number theoryarXiv
Quasi-quantum groups arising from cotensor coquasi-Hopf algebras
Jing Yu, Xiangjun Zhen
arXiv8 Oct 2026PreprintarXiv licenceFull textAlgebra & number theoryarXiv
On stable twist 2-groups of quasi-Hopf algebras
Siu-Hung Ng, Xingting Wang
arXiv29 Oct 2026PreprintCC BY 4.0Full textAlgebra & number theoryarXiv
Hopf quotients of the infinite-dimensional Gaussian pyramid
Takashi Shioya, Shigeaki Yokota
arXiv24 Sep 2026PreprintarXiv licenceFull textGeometry & topology ProbabilityarXiv
Irrationality exponents of logarithmic numbers: Values, quotients, and graded approximation
Gregory V. Chudnovsky
arXiv20 Oct 2026PreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeX RIS

BibTeX

@misc{calderon2026quotients,
  title = {{Quotients of graded quasi-Hopf algebras}},
  author = {Fabio Calderón and César Galindo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.14381},
  eprint = {2607.14381},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.14381},
}

RIS

TY  - UNPB
TI  - Quotients of graded quasi-Hopf algebras
AU  - Fabio Calderón
AU  - César Galindo
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2607.14381
UR  - https://arxiv.org/abs/2607.14381
AB  - We classify the quasi-Hopf ideals of quasi-Hopf algebras faithfully graded by arbitrary groups. Each ideal determines a normal subgroup, recording which degrees are identified in the quotient, together with an invariant ideal in the corresponding neutral component. We refine this description using an ideal of the original neutral component and a retraction of a naturally associated intermediate quotient. We prove that this intermediate quotient splits as the tensor product of its neutral component with the group algebra of the normal subgroup. For fixed subgroup and neutral-component data, the possible ideals, whenever they exist, form a torsor described by equivariant homomorphisms into central group-like elements. Our results require neither finite dimensionality nor bijectivity of the antipode. We apply them to cocentral abelian extensions with possibly infinite grading, finite-dimensional neutral component, and nontrivial reassociator.
ER  -

Abstract

Related

Cite