For cyclic quivers Delta_n, Ext^3 vanishes between any finite-dimensional nilpotent F1-representations while Ext^2 is infinite-dimensional between any pair of simple ones.
arXiv preprint arXiv:2403.07810 , year=
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Biserial fractional Brauer graph algebras are tilting-discrete iff their reduced Brauer graph forms are, and tilting-discrete examples are closed under derived equivalence.
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On higher extensions of quiver representations over $\mathbb{F}_1$
For cyclic quivers Delta_n, Ext^3 vanishes between any finite-dimensional nilpotent F1-representations while Ext^2 is infinite-dimensional between any pair of simple ones.
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Two-term tilting complexes of biserial fractional Brauer graph algebras
Biserial fractional Brauer graph algebras are tilting-discrete iff their reduced Brauer graph forms are, and tilting-discrete examples are closed under derived equivalence.