تقرير
Tensor product of representations of quivers
| العنوان: | Tensor product of representations of quivers |
|---|---|
| المؤلفون: | Das, Pradeep, Dubey, Umesh V., Raghavendra, N. |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry |
| الوصف: | 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 $\tilde{N_1} \times \tilde{N_2}$. Comment: accepted version; to appear in Indagationes Mathematicae |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2305.09159 |
| رقم الأكسشن: | edsarx.2305.09159 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |