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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.09159 |
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Table of Contents:
- In this article, we define the tensor product $V\otimes W$ of a representation $V$ of a quiver $Q$ with a representation $W$ of an another quiver $Q'$, and show that the representation $V\otimes W$ is semistable if $V$ and $W$ are semistable. Over the field of complex numbers, we also describe a relation between the natural line bundles, and between the universal representations on the fine moduli spaces $N_1, N_2$ and $N_3$ of representations of $Q, Q'$ and $Q\otimes Q'$ respectively. We then prove that the internal product $\tilde{Q}\otimes \tilde{Q'}$ of covering quivers is a sub-quiver of the covering quiver $\widetilde{Q\otimes Q'}$. We deduce the relation between stability of the representations $\widetilde{V\otimes W}$ and $\tilde{V} \otimes \tilde{W}$. We also lift the relation between natural line bundles on the product of moduli spaces $\tilde{N_1} \times \tilde{N_2}$.