Projective representations of quivers

Sangwon Park

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 31, 1-5

Abstract:

We prove that P 1   → f   P 2 is a projective representation of a quiver Q = • → • if and only if P 1 and P 2 are projective left R -modules, f is an injection, and f   ( P   1 ) ⊂ P   2 is a summand. Then, we generalize the result so that a representation M 1   → f 1     M 2     → f 2 ⋯ → f n − 2     M n − 1 → f n − 1     M n of a quiver Q = • → • → • ⋯ • → • → • is projective representation if and only if each M i is a projective left R -module and the representation is a direct sum of projective representations.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:840892

DOI: 10.1155/S0161171202108192

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