Related papers: Preprojective algebras and Calabi-Yau duality
In this article we study higher preprojective algebras, showing that various known results for ordinary preprojective algebras generalize to the higher setting. We first show that the quiver of the higher preprojective algebra is obtained…
The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for noncommutative Fourier analysis allowing for that property. It is…
In this paper we study a certain class of central extensions of preprojective algebras of quivers under the name quiver Heisenberg algebras (QHA). There are several classes of algebras introduced before by different researchers from…
We observe that over an algebraically closed field, any finite-dimensional algebra is the endomorphism algebra of an m-cluster-tilting object in a triangulated m-Calabi-Yau category, where m is any integer greater than 2.
Using diagrammatic methods, we define a quiver algebra depending on a prime p and show that it is the algebra underlying the category of tilting modules for SL(2) in characteristic p. Along the way we obtain a presentation for morphisms…
In this paper, we compute the product structure of the Hochschild cohomology of preprojective algebras of quivers of type D and E over a field of characteristic zero.
We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In…
Building on work by Geiss-Leclerc-Schroer and by Buan-Iyama-Reiten-Scott we investigate the link between certain cluster algebras with coefficients and suitable 2-Calabi-Yau categories. These include the cluster-categories associated with…
We focus on quiver Yangians for most generalized conifolds. We construct a coproduct of the quiver Yangian following the similar approach by Guay-Nakajima-Wendlandt. We also prove that the quiver Yangians related by Seiberg duality are…
A triangulated category is said to be Calabi-Yau of dimension d if the dth power of its suspension is a Serre functor. We determine which stable categories of self-injective algebras A of finite representation type are Calabi-Yau and…
The quiver Yangian, an infinite-dimensional algebra introduced recently in arXiv:2003.08909, is the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We introduce trigonometric and elliptic analogues of quiver…
We introduce (n+1)-preprojective algebras of algebras of global dimension n. We show that if an algebra is n-representation-finite then its (n+1)-preprojective algebra is self-injective. In this situation, we show that the stable module…
Crawley-Boevey and Shaw recently introduced a certain multiplicative analogue of the deformed preprojective algebra, which they called the multiplicative preprojective algebra. In this paper we study the moduli space of (semi)stable…
We introduce some new algebraic structures arising naturally in the geometry of Calabi-Yau manifolds and mirror symmetry. We give a universal construction of Calabi-Yau algebras in terms of a noncommutative symplectic DG algebra resolution.…
The goal of this paper is to prove that if Q is a connected non-Dynkin quiver then the preprojective algebra of Q over any field k is Koszul, and has Hilbert series 1/(1-Ct+t^2), where C is the adjacency matrix of the double of Q. (This…
In this paper, we construct certain algebraic correspondences between genus three curves and certain type of Calabi-Yau threefolds which is double coverings of three dimensional projective space. Via this correspondences, the first…
The singular cochain complex of a topological space is a classical object. It is a Differential Graded algebra which has been studied intensively with a range of methods, not least within rational homotopy theory. More recently, the tools…
We consider an orbit category of the bounded derived category of a path algebra of type A_n which can be viewed as a -(m+1)-cluster category, for m >= 1. In particular, we give a characterisation of those maximal m-rigid objects whose…
As a generalization of acyclic 2-Calabi-Yau categories, we consider 2-Calabi-Yau categories with a directed cluster-tilting subcategory; we study their cluster-tilting subcategories and the cluster combinatorics that they encode. We show…
We prove that compact Calabi--Yau varieties with certain isolated singularities are projective. In dimension 3 we do this by analysis, supposing given conifold metrics. In higher dimensions it follows more readily from Ohsawa's degenerate…