All Questions
Tagged with quivers preprojective-algebra
4
questions
4
votes
0
answers
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Realisation of the preprojective algebras as $F(\Delta)/T$ over some quasi-hereditary algebra
Let $A$ be the Auslander algebra of $K[x]/(x^n)$ for some $n \geq 2$, which is quasi-hereditary with some characteristic tilting module $T$.
Dlab and Ringel showed in their paper "The Module ...
- 25.4k
2
votes
0
answers
47
views
Injective morphisms between preprojective representations
Let $Q$ be an acyclic quiver. Is it true that if $P$ is a preprojective representation of $Q$ and $r\geq 0$, there exists $s\geq r$ and a preprojective $P'$ with an injective morphism
$$
P\rightarrow \...
- 323
2
votes
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answers
142
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An equivalence between projective modules over the preprojective algebra and an orbit category
Let $Q$ be a Dynkin quiver, and let $kQ$ be its path algebra over some field k. Let $\Pi$ be the preprojective algebra of $Q$. Then (c.f. Section 7.3 of Keller's On Triangulated Orbit Categories) the ...
- 217
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votes
1
answer
154
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dimension vector of indecomposable module over preprojective algebra
It is well-known that there are finitely many indecomposable module over the preprojective algebra associated to a quiver $Q$ if and only if $Q=A_2,A_3,A_4$ and tame type for $A_5$ and wild for others....
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