PreprintCC BY-SA 4.0arXiv
Graded Kronecker Modules of Constant Rank
Abstract
Let K(n) be the generalized Kronecker quiver, and let (T(n),Ω) be the universal covering of K(n), where n≥ 3 and Ω is a bipartite orientation. We introduce three different types of representations for quiver (T(n),Ω) by K(n): maps are injective in a representation maps are all surjective in a representation, and representations are of constant rank. We use Inj, Sur and GR to denote the corresponding subcategories containing these representations, respectively, and we show that \begin{center} GR= Inj∪Sur. \end{center}
Related
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BibTeX
@misc{liu2026graded,
title = {{Graded Kronecker Modules of Constant Rank}},
author = {Jie Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14240},
eprint = {2609.14240},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14240},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Graded Kronecker Modules of Constant Rank
AU - Jie Liu
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14240
UR - https://arxiv.org/abs/2609.14240
AB - Let K(n) be the generalized Kronecker quiver, and let (T(n),Ω) be the universal covering of K(n), where n≥ 3 and Ω is a bipartite orientation. We introduce three different types of representations for quiver (T(n),Ω) by K(n): maps are injective in a representation maps are all surjective in a representation, and representations are of constant rank. We use Inj, Sur and GR to denote the corresponding subcategories containing these representations, respectively, and we show that \begin{center} GR= Inj∪Sur. \end{center}
ER -