PreprintCC BY 4.0arXiv
Superdecomposable Complete Path Algebras
Abstract
Generalizing the setting of the second author's work on indecomposable modules without nonzero hollow factors, we characterize quivers Q for which the dual algebra R of the path coalgebra of Q, equivalently the complete path algebra, has no nonzero uniform right ideals: this happens exactly when every vertex of Q can reach a vertex emitting at least two distinct arrows. Equivalently, the injective hull E(R) of the right regular module is superdecomposable. These conditions are also equivalent to the path coalgebra having no nonzero hollow factor modules as a left module over its dual algebra.
Related
- On silting theory for complete path algebras
- On the existence of divisible non-injective modules over Leavitt path algebras
- Growth functions of algebras and an application to Leavitt path algebras
- Cohen-Macaulay truncated path and Nakayama algebras
- On some relationships between Leavitt path algebras and Brauer configuration algebras
BibTeX
@misc{hatipoglu2026superdecomposable,
title = {{Superdecomposable Complete Path Algebras}},
author = {Can Hatipoğlu and Christian Lomp},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16746},
eprint = {2610.16746},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16746},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Superdecomposable Complete Path Algebras
AU - Can Hatipoğlu
AU - Christian Lomp
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16746
UR - https://arxiv.org/abs/2610.16746
AB - Generalizing the setting of the second author's work on indecomposable modules without nonzero hollow factors, we characterize quivers Q for which the dual algebra R of the path coalgebra of Q, equivalently the complete path algebra, has no nonzero uniform right ideals: this happens exactly when every vertex of Q can reach a vertex emitting at least two distinct arrows. Equivalently, the injective hull E(R) of the right regular module is superdecomposable. These conditions are also equivalent to the path coalgebra having no nonzero hollow factor modules as a left module over its dual algebra.
ER -