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arXiv · 2209.01043

Relative left Bongartz completions and their compatibility with mutations

Peigen Cao·Yu Wang·Houjun Zhang
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Abstract

In this paper, we introduce relative left Bongartz completions for a given basic $τ$-rigid pair $(U,Q)$ in the module category of a finite dimensional algebra $A$. They give a family of basic $τ$-tilting pairs containing $(U,Q)$ as a direct summand. We prove that relative left Bongartz completions have nice compatibility with mutations. Using this compatibility we are able to study the existence of maximal green sequences under $τ$-tilting reduction. We also explain our construction and some of the results in the setting of silting theory.

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Peigen Cao, Yu Wang, Houjun Zhang. 2023-09-29. Relative left Bongartz completions and their compatibility with mutations. https://doi.org/10.1007/s00209-023-03357-9

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