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The associated graded algebras of biserial fractional Brauer graph algebras

  • Jing Guo
  • Nengqun Li
  • Yuming Liu
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Abstract

For any finite-dimensional algebra A, one can associate a graded algebra (denoted by gr(A)) with the radical filtration of A. An interesting question is to compare the representation theories of A and gr(A). When A is a Brauer graph algebra with defining Brauer graph Γ, we have described the representation type of gr(A) in terms of the information of Γ. In this paper, we describe the representation type of gr(A) when A is a biserial fractional Brauer graph algebra - a notion that properly generalizes a Brauer graph algebra - in terms of the information of the defining biserial fractional Brauer graph Γ of A.

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Cite

BibTeXRIS
BibTeX
@misc{guo2026associated,
  title = {{The associated graded algebras of biserial fractional Brauer graph algebras}},
  author = {Jing Guo and Nengqun Li and Yuming Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25274},
  eprint = {2610.25274},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25274},
}
RIS
TY  - UNPB
TI  - The associated graded algebras of biserial fractional Brauer graph algebras
AU  - Jing Guo
AU  - Nengqun Li
AU  - Yuming Liu
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25274
UR  - https://arxiv.org/abs/2610.25274
AB  - For any finite-dimensional algebra A, one can associate a graded algebra (denoted by gr(A)) with the radical filtration of A. An interesting question is to compare the representation theories of A and gr(A). When A is a Brauer graph algebra with defining Brauer graph Γ, we have described the representation type of gr(A) in terms of the information of Γ. In this paper, we describe the representation type of gr(A) when A is a biserial fractional Brauer graph algebra - a notion that properly generalizes a Brauer graph algebra - in terms of the information of the defining biserial fractional Brauer graph Γ of A.
ER  -