论文标题
指数有限维S^1持久模块的分解
Decomposition of Pointwise Finite-Dimensional S^1 Persistence Modules
论文作者
论文摘要
我们证明，在任意字段上，有限维的S^1持续模块将独特的分解为同构，直接分解为条形码的直接总和和有限的乔丹细胞。这些持久性模块也称为角值或圆形持久性模块。我们允许在S^1上进行环状订单或部分订单，并且在模块上没有其他有限要求。我们还表明，当且仅当它是bar或jordan单元格（在表示理论中，分别是字符串或频带模块）时，当且仅当它是bar或jordan单元时，且仅当它分别是bar或jordan单元时，持久模块是不可分解的。在此过程中，我们对此类不可分解的模块的同构类别进行分类。
We prove that pointwise finite-dimensional S^1 persistence modules over an arbitrary field decompose uniquely, up to isomorphism, into the direct sum of a bar code and finitely-many Jordan cells. These persistence modules have also been called angle-valued or circular persistence modules. We allow either a cyclic order or partial order on S^1 and do not have additional finiteness requirements on the modules. We also show that a pointwise finite-dimensional S^1 persistence module is indecomposable if and only if it is a bar or Jordan cell (a string or a band module, respectively, in representation theory). Along the way we classify the isomorphism classes of such indecomposable modules.
