Singly generated planar algebras of small dimension
Singly generated planar algebras of small dimension
复制标题
单生成的小维平面代数
DOI：
10.1215/s0012-7094-00-10112-3
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发表时间：
2000
影响因子：
2.5
通讯作者：
V. Jones
中科院分区：
文献类型：
--
作者：
D. Bisch;V. Jones
0.导论.一个子因子N M产生了一组强大的不变量，可以通过几种方式成功地接近。(See例如，[B2]、[EK]、[FRS]、[GHaJ]、[H]、[Iz]、[JSu]、[Lo1]、[Lo2]、[Oc1]、[Oc2]、[Po1]、[Po2]、[Po3]、[Po4]、[Wa]、[We1]和[We2]）。一种特殊的方法建议将一种特殊类型的子因子作为“最简单的”。例如，在Haagerup的方法[H]中，小指数的子因子是最简单的。在[J2]中，发展了一种图形语言，其中不变量表现为分次向量空间V =（Vn）n≥0，其元素可以以平面但相当任意的方式组合。例如，在图中，
0. Introduction. A subfactorN ⊂M gives rise to a powerful set of invariants that can be approached successfully in several ways. (See, for instance, [B2], [EK], [FRS], [GHaJ], [H], [Iz], [JSu], [Lo1], [Lo2], [Oc1], [Oc2], [Po1], [Po2], [Po3], [Po4], [Wa], [We1], and [We2]). A particular approach suggests a particular kind of subfactor as the “simplest.” For instance, in Haagerup’s approach [H], subfactors of small index are the simplest. In [J2], a pictorial language is developed in which the invariants appear as a graded vector space V = (Vn)n≥0 whose elements can be combined in planar, but otherwise quite arbitrary, ways. Thus, for instance, in the diagram