Quivers without loops admit global dimension 2
Nicolas Poettering
TL;DR
This paper proves that for any finite loopless quiver, there exists an algebra with global dimension at most two that is (strongly) quasi-hereditary, and also constructs other such algebras with higher global dimensions.
Contribution
It demonstrates that all finite quivers without loops admit a strongly quasi-hereditary algebra with global dimension at most two, and provides constructions for algebras with larger global dimensions.
Findings
Existence of a strongly quasi-hereditary algebra with global dimension ≤ 2 for any loopless finite quiver.
Construction of other (strongly) quasi-hereditary algebras with higher global dimensions.
Algebras are of the form kQ/I with suitable admissible ideals I.
Abstract
Let be a finite quiver without loops. Then there is an admissible ideal such that the algebra has global dimension at most two and is (strongly) quasi-hereditary. In addition some other (strongly) quasi-hereditary algebras are constructed with bigger global dimension.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Rings, Modules, and Algebras