Abstract representation theory of Dynkin quivers of type A
Abstract representation theory of Dynkin quivers of type A
复制标题
A型Dynkin箭袋的抽象表示理论
DOI：
10.1016/j.aim.2016.02.018
复制
发表时间：
2014
影响因子：
1.7
通讯作者：
J. Šťovíček
中科院分区：
文献类型：
--
作者：
Moritz Groth;J. Šťovíček
我们研究了抽象稳定同伦理论中A型Dynkin箭图的表示理论，包括与域、环、方案、微分分次代数和环谱相关的理论。反射函子，（部分）Coxeter函子，和塞尔函子定义在这种普遍性和这些等价性所示的诱导普遍倾斜模块，某些明确构建的谱双模。事实上，这些泛倾斜模是经典倾斜复形的谱加细。作为结果，我们得到分裂满射谱皮卡广群导出皮卡广群在任意域上。这些结果是一个更一般的演算的谱双模和容许态射的稳定导子的后果。作为进一步的应用，这种演算，我们得到的例子普遍倾斜模块，这是新的，即使在上下文中的陈述在一个领域。这包括米田双模网格类别编码所有其他通用倾斜模块，并导致频谱塞尔对偶结果。最后，利用线性方向的A n-箭图的抽象表示理论，我们构造了稳定导子中的典范高阶三角剖分，从而也构造了稳定模型范畴和稳定∞-范畴中的典范高阶三角剖分.
We study the representation theory of Dynkin quivers of type A in abstract stable homotopy theories, including those associated to fields, rings, schemes, differential-graded algebras, and ring spectra. Reflection functors,(partial) Coxeter functors, and Serre functors are defined in this generality and these equivalences are shown to be induced by universal tilting modules, certain explicitly constructed spectral bimodules. In fact, these universal tilting modules are spectral refinements of classical tilting complexes. As a consequence we obtain split epimorphisms from the spectral Picard groupoid to derived Picard groupoids over arbitrary fields. These results are consequences of a more general calculus of spectral bimodules and admissible morphisms of stable derivators. As further applications of this calculus we obtain examples of universal tilting modules which are new even in the context of representations over a field. This includes Yoneda bimodules on mesh categories which encode all the other universal tilting modules and which lead to a spectral Serre duality result. Finally, using abstract representation theory of linearly oriented A n-quivers, we construct canonical higher triangulations in stable derivators and hence, a posteriori, in stable model categories and stable∞-categories.
通过稳定同伦理论的树木倾斜理论
影响因子：
0.8
作者：
Moritz with Stovicek
通讯作者：
Moritz with Stovicek
幺半群导数中痕量的可加性
DOI：
10.1017/is014005011jkt262
发表时间：
2014
期刊：
arXiv: Algebraic Topology
影响因子：
--
作者：
Moritz with Ponto;Shulman
通讯作者：
Shulman