Quiver representation theory MOC

Quiver representation

A -representation of a quiver may be characterized in several different ways: quiv

1. A quiver homomorphism from onto a -linear quiver;
2. A functor from the free category to Category of vector spaces;
3. A module over the Path algebra .

where the equivalence of ^R2 and ^R3 follows from Module over a category ring. Generally, it is useful to think of a quiver representation as a -representations which is also a -graded vector space.

Often we are only interested in finite-dimensional representations, i.e. those of the form . We might also consider a Matrix quiver representation .

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