相关论文: The double Ringel-Hall algebra on a hereditary abe…

Let $\mathcal{A}$ be an arbitrary hereditary abelian category that may not have enough projective objects. For example, $\mathcal{A}$ can be the category of finite-dimensional representations of a quiver or the category of coherent sheaves…

Let $t$ be a positive integer and $\mathcal{A}$ a hereditary abelian category satisfying some finiteness conditions. We define the semi-derived Ringel-Hall algebra of $\mathcal{A}$ from the category $\mathcal{C}_{\mathbb{Z}/t}(\mathcal{A})$…

Let $A$ be a tame hereditary algebra over a finite field $k$ with $q$ elements, and ${\bar{A}}$ be the duplicated algebra of $A$. In this paper, we investigate the structure of Ringel-Hall algebra $\mathscr{H} (\bar{A})$ and of the…

For a finitary hereditary abelian category $\mathcal{A}$, we define a derived Hall algebra of its root category by counting the triangles and using the octahedral axiom, which is proved to be isomorphic to the Drinfeld double of Hall…

To an abelian category A of homological dimension 1 satisfying certain finiteness conditions, one can associate an algebra, called the Hall algebra. Kapranov studied this algebra when A is the category of coherent sheaves over a smooth…

For a given hereditary abelian category satisfying some finiteness conditions, in certain twisted cases it is shown that the modified Ringel-Hall algebra is isomorphic to the naive lattice algebra and there exists an epimorphism from the…

From a category $\mathcal{A}$ with an involution $\varrho$, we introduce $\varrho$-complexes, which are a generalization of (bounded) complexes, periodic complexes and modules of $\imath$quiver algebras. The homological properties of the…

We define and study the category $Coh_n(\Pone)$ of normal coherent sheaves on the monoid scheme $\Pone$ (equivalently, the $\mathfrak{M}_0$-scheme $\Pone / \fun$ in the sense of Connes-Consani-Marcolli \cite{CCM}). This category resembles…

In the present paper, we introduce two-dimensional categorified Hall algebras of smooth curves and smooth surfaces. A categorified Hall algebra is an associative monoidal structure on the stable $\infty$-category…

Let $\mathcal{A}$ be an arbitrary hereditary abelian category. Lu and Peng defined the semi-derived Ringel-Hall algebra $SH(\mathcal{A})$ of $\mathcal{A}$ and proved that $SH(\mathcal{A})$ has a natural basis and is isomorphic to the…

We consider the category $\operatorname{Qcoh}\mathbb{X}$ of quasicoherent sheaves where $\mathbb{X}$ is a weighted noncommutative regular projective curve over a field $k$. This category is a hereditary, locally noetherian Grothendieck…

Let $\A$ be a finitary hereditary abelian category with enough projectives. We study the Hall algebra of complexes of fixed size over projectives. Explicitly, we first give a relation between Hall algebras of complexes of fixed size and…

For any finite-dimensional algebra $A$ over a field $k$ with finite global dimension, we investigate the root category $\cR_A$ as the triangulated hull of the 2-periodic orbit category of $A$ via the construction of B. Keller in "On…

Inspired by recent work of Bridgeland, from the category C^b(E) of bounded complexes over an exact category E satisfying certain finiteness conditions, we construct an associative unital "semi-derived Hall algebra" SDH(E). This algebra is…

Given a Frobenius category $\mathcal{F}$ satisfying certain finiteness conditions, we consider the localization of its Hall algebra $\mathcal{H(F)}$ at the classes of all projective-injective objects. We call it the {\it "semi-derived Hall…

In this paper we define the modified Ringel-Hall algebra $\cm\ch(\ca)$ of a hereditary abelian category $\ca$ from the category $C^b(\mathcal{A})$ of bounded $\mathbb{Z}$-graded complexes. Two main results have been obtained. One is to give…

We define the cohomological Hall algebra ${AHA}_{Higgs(X)}$ of the ($2$-dimensional) Calabi-Yau category of Higgs sheaves on a smooth projective curve $X$, as well as its nilpotent and semistable variants, in the context of an arbitrary…

We construct from a finitary exact category with duality a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure of the category. We study in detail Hall modules arising from the…

Let T be a tilting object in a triangulated category equivalent to the bounded derived category of a hereditary abelian category with finite dimensional homomorphism spaces and split idempotents. This text investigates the strong global…

We define the spherical Hecke algebra H for an almost split Kac-Moody group G over a local non-archimedean field. We use the hovel I associated to this situation, which is the analogue of the Bruhat-Tits building for a reductive group. The…