Representation Theory of Curried Algebras and Non-primality of Certain Symmetric Ideals

Abstract

This thesis consists of two separate parts. The first part (Chapter II to Chapter VI) is about the representation theory of curried algebras, and the second part (Chapter VII) gives a proof of non-primality of certain symmetric ideals. In Chapter II, we review some preliminary background on the representation theory of curried algebras. We summarize results from [SS2] and [SS3], and present definitions that will be used later, such as triangular categories, the Brauer category, etc. We end the chapter by summarizing comparison theorems associated to modules of a curried algebras over a standard FB-module.