论文标题
关于对称颤抖的辅助和K理论厅代数
On cohomological and K-theoretical Hall algebras of symmetric quivers
论文作者
论文摘要
我们简要审查了共同体厅代数COHA $ \ MATHCAL {H} $和K理论厅代数Kha $ \ Mathcal {R} $与Quivers相关。在对称颤音的情况下，我们表明存在代数的同态（从Chern角色图获得）$ \ Mathcal {r} \ to \ hat {\ hat {\ Mathcal {h}}^σ$ wher $ \ MATHCAL {H} $。此外，我们建立了``本地有限''分级模块的类别的等效性。本地有限$ \ hat的示例{\ Mathcal {h}}}^σ$ - ，resp。 $ \ MATHCAL {R} _ {\ MATHBB Q} $ - 模块自然而然地作为同事，resp。 K理论，框架的模仿空间。
We give a brief review of the cohomological Hall algebra CoHA $\mathcal{H}$ and the K-theoretical Hall algebra KHA $\mathcal{R}$ associated to quivers. In the case of symmetric quivers, we show that there exists a homomorphism of algebras (obtained from a Chern character map) $\mathcal{R}\to \hat{\mathcal{H}}^σ$ where $\hat{\mathcal{H}}^σ$ is a Zhang twist of the completion of $\mathcal{H}$. Moreover, we establish the equivalence of categories of ``locally finite'' graded modules $\hat{\mathcal{H}}^σ-{\rm Mod}_{lf}\simeq \mathcal{R}_{\mathbb Q}-{\rm Mod}_{lf}$. Examples of locally finite $\hat{\mathcal{H}}^σ$-, resp. $\mathcal{R}_{\mathbb Q}$- modules appear naturally as the cohomology, resp. K-theory, of framed moduli spaces of quivers.
