论文标题
非共同张量三角几何和用于支撑图的张量产品特性
Noncommutative tensor triangular geometry and the tensor product property for support maps
论文作者
论文摘要
有限维数代数的共同体支持图是否具有张量产品的属性，这引起了很多关注，这是对有限组方案表示的早期发展。许多作者专注于通过直接参数获得正面和负面结果的具体情况。 在本文中，我们证明，在更广泛的三角形类别的更广泛环境中，研究涉及张量产品特性的问题是很自然的。我们通过证明通用支持基准的张量产品属性等于分类频谱的完整性，从而给出了内在的表征。从这些结果中，一个人获得了其他支持数据的信息，包括共同学数据。事实证明，两个定理在某些一般环境中给出了竞争的灵巧性和不完整的灵巧性。 作为方法的例证，我们给出了张量的张量产品特性上的Negron和Pevtsova的近期猜想，用于用于所有复杂简单的LIE代数的小量子Borel代数。
The problem of whether the cohomological support map of a finite dimensional Hopf algebra has the tensor product property has attracted a lot of attention following the earlier developments on representations of finite group schemes. Many authors have focussed on concrete situations where positive and negative results have been obtained by direct arguments. In this paper we demonstrate that it is natural to study questions involving the tensor product property in the broader setting of a monoidal triangulated category. We give an intrinsic characterization by proving that the tensor product property for the universal support datum is equivalent to complete primeness of the categorical spectrum. From these results one obtains information for other support data, including the cohomological one. Two theorems are proved giving compete primeness and non-complete primeness in certain general settings. As an illustration of the methods, we give a proof of a recent conjecture of Negron and Pevtsova on the tensor product property for the cohomological support maps for the small quantum Borel algebras for all complex simple Lie algebras.
