In this short note we show that the size of an exceptional sequence in the module category of a finite dimensional algebra $A$ can be arbitrarily large in comparison to the number of isomorphism classes of simple $A$-modules. We do so by constructing an exceptional sequence in the module category of the Auslander algebra of the path algebra of the linearly oriented $\mathbb{A}_n$ quiver.
On the radical of the module category of an endomorphism algebra
Infinite dimensional representations of finite dimensional algebras and amenability
The geometry of uniserial representations of finite dimensional algebras III: Finite uniserial type
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