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Lifting A∞-structures through coverings with applications to fractional Brauer graph algebras

  • Bohan Xing
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Abstract

Under suitable group actions, it is known that A∞-structures descend to orbit categories. We study the converse problem of lifting an A∞-structure to a prescribed covering. We show that a compatible group grading determines a canonical lift, uniquely characterized by the strictness of the covering projection. As an application, we construct A∞-categories associated with admissible fractional Brauer graph algebras by lifting Brauer graph A∞-categories. Their geometric data augment the surface models of Brauer graph algebras with a Nakayama character encoding the covering. We prove that admissible fractional Brauer graph algebras with equivalent geometric data are derived equivalent. Furthermore, we establish a set of combinatorial derived invariants and prove their completeness in reduced genus zero and in reduced genus at least two when the defining ribbon graph is non-bipartite.

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Cite

BibTeXRIS
BibTeX
@misc{xing2026lifting,
  title = {{Lifting $A_\infty$-structures through coverings with applications to fractional Brauer graph algebras}},
  author = {Bohan Xing},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27660},
  eprint = {2609.27660},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27660},
}
RIS
TY  - UNPB
TI  - Lifting A_∞-structures through coverings with applications to fractional Brauer graph algebras
AU  - Bohan Xing
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27660
UR  - https://arxiv.org/abs/2609.27660
AB  - Under suitable group actions, it is known that A_∞-structures descend to orbit categories. We study the converse problem of lifting an A_∞-structure to a prescribed covering. We show that a compatible group grading determines a canonical lift, uniquely characterized by the strictness of the covering projection. As an application, we construct A_∞-categories associated with admissible fractional Brauer graph algebras by lifting Brauer graph A_∞-categories. Their geometric data augment the surface models of Brauer graph algebras with a Nakayama character encoding the covering. We prove that admissible fractional Brauer graph algebras with equivalent geometric data are derived equivalent. Furthermore, we establish a set of combinatorial derived invariants and prove their completeness in reduced genus zero and in reduced genus at least two when the defining ribbon graph is non-bipartite.
ER  -