Abstract Extensions of association schemes and table algebras have been studied in many papers in the last two decades. A remarkable operation (the Blau-construction) on two table algebras in [3] provides an important method to construct the extension of table algebras. The wedge-direct sum of a sequence of table algebras introduced in Part I (see [14] ) is a useful tool for the study of structures and characterizations of table algebras. Using the wedge-direct sum of a sequence of table algebras, in Part I we gave a new perspective on the Blau-construction, and obtained a clear description of the structure of table algebras constructed by recursively applying the Blau-construction. p-table algebras (p-schemes) are an important class of table algebras (association schemes). In this part we will give the characterization and classification of a class of p-table algebras, by showing that they are isomorphic to the wedge-direct sum of a sequence of group algebras of finite p-groups. In order to determine whether two distinct sequences of table algebras yield the isomorphic wedge-direct sums or not, we will need to discuss the redundancy of the wedge-direct sum, and prove a Krull-Schmidt type theorem. Applications to association schemes will also be discussed.

中文翻译：

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表代数的楔形直接求和及其在关联方案中的应用，II

摘要 在过去的 20 年中，许多论文都研究了关联方案和表代数的扩展。[3]中对两个表代数的一个显着操作（Blau-construction）提供了一个重要的方法来构造表代数的扩展。第一部分中介绍的表代数序列的楔形直接和（参见 [14]）是研究表代数的结构和表征的有用工具。使用一系列表代数的楔形直接和，在第一部分中，我们对Blau-构造给出了一个新的视角，并通过递归应用Blau-构造得到了对表代数结构的清晰描述。p-表代数（p-schemes）是一类重要的表代数（关联方案）。在这一部分，我们将给出一类 p 表代数的表征和分类，通过证明它们同构于有限 p 群的群代数序列的楔形直接和。为了确定两个不同的表代数序列是否会产生同构的楔形直和，我们需要讨论楔形直和的冗余，并证明一个 Krull-Schmidt 型定理。还将讨论对关联计划的应用。