PreprintCC BY 4.0arXiv
Derived tame monomial algebras
Abstract
We prove that a finite-dimensional connected monomial algebra over an algebraically closed field is derived tame if and only if every finite connected convex subcategory of its universal cover has non-negative Euler form. Derived tameness is also equivalent to tameness of its repetitive category and trivial extension. For one-cycle algebras, this condition is equivalent to the non-negativity on ℝ of |Q0| explicitly computable polynomials in ℚ[t]. This gives a finite algorithm for deciding derived tameness. We also construct an infinite family of derived-tame one-cycle string algebras with minimal cubic relations, no two of which are derived equivalent.
Related
- Representation-tame Geiß-Leclerc-Schröer algebras and a revised GLS conjecture on root systems
- KMS and ground states for the normalized dynamics of the tame C*-algebras 𝒪m,n
- Isometric rigidity of complete Pick algebras on monomial varieties
- Christophersen's problem for monomial algebras
- Stable equivalence of quadratic monomial algebras
BibTeX
@misc{fonseca2026derived,
title = {{Derived tame monomial algebras}},
author = {Marlon Pimenta Fonseca and Zheng Xin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41759},
eprint = {2610.41759},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41759},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Derived tame monomial algebras
AU - Marlon Pimenta Fonseca
AU - Zheng Xin
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41759
UR - https://arxiv.org/abs/2610.41759
AB - We prove that a finite-dimensional connected monomial algebra over an algebraically closed field is derived tame if and only if every finite connected convex subcategory of its universal cover has non-negative Euler form. Derived tameness is also equivalent to tameness of its repetitive category and trivial extension. For one-cycle algebras, this condition is equivalent to the non-negativity on ℝ of |Q_0| explicitly computable polynomials in ℚ[t]. This gives a finite algorithm for deciding derived tameness. We also construct an infinite family of derived-tame one-cycle string algebras with minimal cubic relations, no two of which are derived equivalent.
ER -