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arXiv · 2610.25274

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 $\mathrm{gr}(A)$) with the radical filtration of $A$. An interesting question is to compare the representation theories of $A$ and $\mathrm{gr}(A)$. When $A$ is a Brauer graph algebra with defining Brauer graph $Γ$, we have described the representation type of $\mathrm{gr}(A)$ in terms of the information of $Γ$. In this paper, we describe the representation type of $\mathrm{gr}(A)$ 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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Jing Guo, Nengqun Li, Yuming Liu. 2026-10-18. The associated graded algebras of biserial fractional Brauer graph algebras. https://arxiv.org/abs/2610.25274

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