Derivation based noncommutative geometry of quiver path algebras
Abstract
In this paper, we study derivation based noncommutative geometry of path algebras arising from quivers by identifying a Lie algebra of derivations from which a differential calculus is constructed. We show that properties of the differential calculus are intimately connected with the structure of the quiver. In particular, by introducing the notion of a separating quiver, we find a condition on the quiver which is equivalent to the module of differential forms being a projective bimodule. For such quivers, one can construct bimodule connections, as well as bimodule forms which serve as noncommutative analogues of the Riemannian metric. As an illustration of the above concepts, we present a class of quivers for which one can construct Levi-Civita connections, i.e. torsion free connections compatible with a bimodule form.
Related
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- Quiver Demazure algebras I: Residue descent, finite quotients, and PBW bases
- The center conjecture for cyclotomic Hecke algebras and cohomology of quiver varieties
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BibTeX
@misc{arnlind2026derivation,
title = {{Derivation based noncommutative geometry of quiver path algebras}},
author = {Joakim Arnlind and Victor Hildebrandsson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16300},
eprint = {2610.16300},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16300},
}
RIS
TY - UNPB
TI - Derivation based noncommutative geometry of quiver path algebras
AU - Joakim Arnlind
AU - Victor Hildebrandsson
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16300
UR - https://arxiv.org/abs/2610.16300
AB - In this paper, we study derivation based noncommutative geometry of path algebras arising from quivers by identifying a Lie algebra of derivations from which a differential calculus is constructed. We show that properties of the differential calculus are intimately connected with the structure of the quiver. In particular, by introducing the notion of a separating quiver, we find a condition on the quiver which is equivalent to the module of differential forms being a projective bimodule. For such quivers, one can construct bimodule connections, as well as bimodule forms which serve as noncommutative analogues of the Riemannian metric. As an illustration of the above concepts, we present a class of quivers for which one can construct Levi-Civita connections, i.e. torsion free connections compatible with a bimodule form.
ER -