A Serre Relation in the $K$-theoretic Hall algebra of surfaces
英文摘要：
We prove a Serre relation in the $K$-theoretic Hall algebra of surfaces constructed by Kapranov-Vasserot and the second author.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
环路空间形式化与K理论量子Serre对偶
Loop Space Formalism and K-Theoretic Quantum Serre Duality
本文证明了亏格零K理论置换不变Gromov-Witten理论的量子Serre对偶，通过扩展环路空间与big $\mathcal{J}$-函数形式化，重新解释水平结构，并将其推广至旗流形上的非本原向量丛。
math.AG
K-theoretic Hall algebras of quivers with potential as Hopf algebras
For $(Q,W)$ a symmetric quiver with potential satisfying a Künneth-type condition, we construct (positive and negative) extensions of its K-theoretic Hall algebra which are bialgebras. In particular, there are bialgebra extensions of preprojective KHAs of a quiver $Q$ and one can construct their Drinfeld double algebra.
math.AGmath.QAmath.RT
Categorical and K-theoretic Hall algebras for quivers with potential
Given a quiver with potential $(Q,W)$, Kontsevich-Soibelman constructed a Hall algebra on the critical cohomology of the stack of representations of $(Q,W)$. Special cases of this construction are related to work of Nakajima, Varagnolo, Schiffmann-Vasserot, Maulik-Okounkov, Yang-Zhao etc. about geometric constructions of Yangians and their representations; indeed, given a quiver $Q$, there exists an associated pair $\left(\widetilde{Q},\widetilde{W}\right)$ whose CoHA is conjecturally the positive half of the Maulik-Okounkov Yangian $Y_{\text{MO}}(\mathfrak{g}_Q)$. For a quiver with potential …
math.AGmath.QAmath.RT
$K$-理论霍尔代数与色姆分支
$K$-theoretic Hall algebras and Coulomb branches
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Simion Stoilow Institute of Mathematics (IMAR)（西莫恩·斯托伊洛数学研究所）
本文通过洗牌代数解释，构建了一个从合适解释的双重环-nilpotent $K$-理论霍尔代数到quiver规范理论色姆分支代数的满同态，解决了霍尔代数与色姆分支之间的联系问题。
hep-thmath-phmath.AG
On the $K$-theoretic Hall algebra of a surface
In this paper, we define the $K$-theoretic Hall algebra for $0$-dimensional coherent sheaves on a smooth projective surface, prove that the algebra is associative and construct a homomorphism to a redefined shuffle algebra analogous to Negut.
math.AG
上同调Hall代数与K理论Hall代数的比较
Comparison of Cohomological and K-theoretical Hall algebra
本文为对称quiver的K理论Hall代数到上同调Hall代数扭曲的比较代数态射提供了更具概念性的构造，并将该结果推广至带势quiver。
math.AGmath.KTmath.RA
更多相关论文收起更多论文
带势箭图的K理论Hall代数的生成元
Generators for K-theoretic Hall algebras of quivers with potential
本文利用半正交分解技术为带势箭图的K理论Hall代数(KHAs)的商构造并证明了PBW型定理，同时给出了其生成元空间的交K理论描述。
math.AGmath.RT
轮条件与K理论Hall代数
The Wheel Conditions and K-theoretic Hall Algebras
Beijing Institute of Technology（北京理工大学）
本文通过仿射平面上的K理论Hall代数，给出了Feigin-Odesskii提出的轮条件的几何实现。
math.AG
Generators for categorical Hall algebras of surfaces
For a smooth surface $S$, Porta-Sala defined a categorical Hall algebra generalizing previous work in K-theory of Zhao and Kapranov-Vasserot. We construct semi-orthogonal decompositions for categorical Hall algebras of points on $S$. We refine these decompositions in K-theory for a topological K-theoretic Hall algebra.
math.AGmath.RT
Geometric derived Hall algebra
We give a geometric formulation of Toën's derived Hall algebra by constructing Grothendieck's six operations for the derived category of lisse-étale constructible sheaves on the derived stacks of complexes. Our formulation is based on an variant of Laszlo and Olsson's theory of derived categories and six operations for algebraic stacks. We also give an $\infty$-theoretic explanation of the theory of derived stacks, which was originally constructed by Toën and Vezzosi in terms of model theoretical language.
math.AGmath.QA
K-theoretic Hall algebras for quivers with potential
Given a quiver with potential $(Q,W)$, Kontsevich-Soibelman constructed a Hall algebra on the cohomology of the stack of representations of $(Q,W)$. As shown by Davison-Meinhardt, this algebra comes with a filtration whose associated graded algebra is supercommutative. A special case of this construction is related to work of Nakajima, Varagnolo, Maulik-Okounkov etc. about geometric constructions of Yangians and their representations; indeed, given a quiver $Q$, there exists an associated pair $(\widetilde{Q},\widetilde{W})$ for which the CoHA is conjecturally the positive half of the Yangian …
math-phmath.AGmath.MP
Two-dimensional categorified Hall algebras
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 $\mathsf{Coh}^{\mathsf{b}}(\mathbb{R}\mathsf{M})$ of complexes of sheaves with bounded coherent cohomology on a derived moduli stack $\mathbb{R}\mathsf{M}$. In the surface case, $\mathbb{R}\mathsf{M}$ is a suitable derived enhancement of the moduli stack $\mathsf{M}$ of coherent sheaves on the surface. This construction categorifies the K-theoretical and cohomological Hall algebras of…
hep-thmath.AGmath.AT
