Tensor product of representations of quivers

In this article, we define the tensor product V (R) W of a representation V of a quiver Q with a representation W of an another quiver Q ' , and show that the representation V (R) W is semistable if V and W are semistable. We give a relation between the universal representations on the fine moduli spaces N 1 , N 2 and N 3 of representations of Q , Q ' and Q (R) Q ' respectively over arbitrary algebraically closed fields. We further describe a relation between the natural line bundles on these moduli spaces when Q ' of covering the base is the field of complex numbers. We then prove that the internal product quivers is a sub -quiver of the covering quiver Q (R) Q ' . We deduce the relation between stability of the representations V (R) W and V (R) W , where V denotes the lift of the representation V of Q to the covering quiver Q . We also lift the relation between the natural line bundles on the product of moduli Q (R) spaces (c) 2024 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved. N 1 x N 2 .