In this paper, we study a preprojective algebra for quivers decorated with k-algebras and
bimodules, which generalizes work of Gabriel for ordinary quivers, work of Dlab and Ringel …

We prove that multiplicative preprojective algebras, defined by Crawley-Boevey and Shaw,
are 2-Calabi–Yau algebras, in the case of quivers containing unoriented cycles. If the quiver …

Quivers play an important role in the representation theory of algebras, with a key ingredient
being the path algebra and the preprojective algebra. Quiver grassmannians are varieties of …

Given a noncommutative Hamiltonian space $ A $, we show that the conjecture``{\it
quantization commutes with reduction}''holds on $ A $. We also construct a semi-product …

Following the article of CM Ringel we introduce preprojective algebras of a Dynkin quiver $
Q $ starting from three definitions which, despite concerning completely different algebraic …

Associated to each finite subgroup Γ of \ttSL_2(C) there is a family of noncommutative
algebras O^τ(Γ), which is a deformation of the coordinate ring of the Kleinian singularity …

Preprojective algebras [Pi] q of quivers Q were introduced by Gelfand and Ponomarev in
1979 in order to provide a model for quiver representations (in the special case of finite …

In [math. AG/0010030; Math. Z., to appear] R. Bocklandt and the author proved that certain
quotient varieties of representations of deformed preprojective algebras are coadjoint orbits …

Let $\Gamma\in\mathrm {SL} _2 (\mathbb {C}) $ be a finite subgroup. We introduce a class
of projective noncommutative surfaces $\mathbb {P}^ 2_I $, indexed by a set of irreducible …

The first part of this memoir assigns hyperplane arrangements to any choice of vertices in a
Coxeter graph, by taking an intersection arrangement inside a Tits cone. For each such …