Koszulity and the Hilbert series of preprojective algebras
نویسندگان
چکیده
منابع مشابه
Koszulity and the Hilbert Series of Preprojective Algebras
The goal of this paper is to prove that if Q is a connected non-Dynkin quiver then the preprojective algebra ΠQ(k) of Q over any field k is Koszul, and has Hilbert series (1 − Ct+ t2)−1, where C is the adjacency matrix of the double Q̄ of Q. We also prove a similar result for the partial preprojective algebra ΠQ,J(k) of any connected quiver Q, where J ⊂ I is a subset of the set I of vertices of ...
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In this thesis, we investigate two ways of generalising the preprojective algebra. First, we introduce the multiplicative preprojective algebra, Λ(Q), which is a multiplicative analogue of the deformed preprojective algebra, introduced by Crawley-Boevey and Holland. The special case q = 1 is the undeformed multiplicative preprojective algebra, which is an analogue of the ordinary (undeformed) p...
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(1) If there is an indecomposable representation of dimension v, then v is a root. (2) If v is a real root, then there is a unique (up to an isomorphism) indecomposable representation of dimension v. (3) If v is primitive (meaning that GCD(vi) = 1) and there is an indecomposable representation of dimension v, then pv, the number of parameters for the isomorphism classes of indecomposable repres...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2007
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2007.v14.n4.a4