相关论文: Preprojective algebras and Calabi-Yau duality

We compute the Hochschild homology and cohomology, and cyclic homology, of almost Calabi-Yau algebras for SU(3) ADE graphs. These almost Calabi-Yau algebras are a higher rank analogue of the pre-projective algebras for Dynkin diagrams,…

These notes contain a brief introduction to the construction of toric Calabi--Yau hypersurfaces and complete intersections with a focus on issues relevant for string duality calculations. The last two sections can be read independently and…

We define a family of 3-Calabi-Yau algebras by potentials. For some of these algebras, we explicitly compute the Hochschild homology with the help of Poisson homology. The point is that the Poisson potential has non-isolated singularities.

D.Happel and L.Unger defined a partial order on the set of basic tilting modules. We study the poset of basic pre-projective tilting modules over path algebra of infinite type. First we will give a criterion for Ext-vanishing for…

We introduce a notion of pre-alternative algebra which may be seen as an alternative algebra whose product can be decomposed into two pieces which are compatible in a certain way. It is also the "alternative" analogue of a dendriform…

We compare and generalise the various geometric constructions (due to Ringel, Lusztig, Schofield, Bozec, Davison...) of the unipotent generalised Kac-Moody algebra associated with an arbitrary quiver. These constructions are interconnected…

We define a family of homomorphisms on a collection of convolution algebras associated with quiver varieties, which gives a kind of coproduct on the Yangian associated with a symmetric Kac-Moody Lie algebra. We study its property using…

A Com-PreLie bialgebra is a commutative bialgebra with an extra preLie product satisfying some compatibilities with the product and coproduct. We here give a classification of connected, cocommutative Com-PreLie bialgebras over a field of…

In this article we prove that there exists an explicit bijection between nice $d$-pre-Calabi-Yau algebras and $d$-double Poisson differential graded algebras, where $d \in \mathbb{Z}$, extending a result proved by N. Iyudu and M.…

We study the preprojective cohomological Hall algebra (CoHA) introduced by the authors in an earlier work for any quiver $Q$ and any one-parameter formal group $\mathbb{G}$. In this paper, we construct a comultiplication on the CoHA, making…

We compare two cohomological Hall algebras (CoHA). The first one is the preprojective CoHA introduced by the authors in arXiv:1407.7994 associated to each quiver Q, and each algebraic oriented cohomology theory A. It is defined as the…

In this article, a new construction of derived equivalences is given. It relates different endomorphism rings and more generally cohomological endomorphism rings - including higher extensions - of objects in triangulated categories. These…

There is a homotopy hypercommutative algebra structure on the cohomology of a Calabi-Yau variety. The truncation of this homotopy hypercommutative algebra to a strict hypercommutative algebra is well-known as a mathematical realization of…

We define $n$-angulated categories by modifying the axioms of triangulated categories in a natural way. We show that Heller's parametrization of pre-triangulations extends to pre-$n$-angulations. We obtain a large class of examples of…

In this paper, we prove that relation-extensions of quasi-tilted algebras are 2-Calabi-Yau tilted. With the objective of describing the module category of a cluster-tilted algebra of euclidean type, we define the notion of reflection so…

For any valued quiver, by using BGP-reflection functors, an injection from the set of preprojective objects in the cluster category to the set of cluster variables of the corresponding cluster algebra is given, the images are called…

The Attractor Conjecture for Calabi-Yau moduli spaces predicts the algebraicity of the moduli values of certain isolated points picked out by Hodge-theoretic conditions. We provide a family of counterexamples to the Attractor Conjecture in…

This note gives a one-to-one correspondence between the equivalence classes of a certain type of 2-dimensional Calabi-Yau categories, and certain type of quivers, This is an analogue of the result in Stability structures, motivic…

The most impressively prolific exploration of superstring models (aiming for our physical reality) has been focused on worldsheet-supersymmetric gauged linear sigma models and the closely associated complex-algebraic toric geometry. Mirror…

Recently, Bocklandt proved a conjecture by Van den Bergh in its graded version, stating that a graded quiver algebra (with relations) which is Calabi-Yau of dimension 3 is defined from a homogeneous potential W. In this paper, we prove that…