What is "character theory"

n. The branch of abstract algebra dealing with group characters.

This article refers to the use of the term character theory in mathematics. For the media studies definition, see Character theory (Media). For related senses of the word character, see Character (mathematics).

In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix. The character carries the essential information about the representation in a more condensed form. Georg Frobenius initially developed representation theory of finite groups entirely based on the characters, and without any explicit matrix realization of representations themselves. This is possible because a complex representation of a finite group is determined (up to isomorphism) by its character. The situation with representations over a field of positive characteristic, so-called "modular representations", is more delicate, but Richard Brauer developed a powerful theory of characters in this case as well. Many deep theorems on the structure of finite groups use characters of modular representations.

A character theory is used for understanding media, such as print or electronic media texts or productions such as films and plays. It is useful for analysing and understanding media in which people take on the role of an actor or social actor. Character theories are popular with academics teaching and researching media and film studies. They assist in the appreciation of the structure of different types of media and the roles of the characters, fictional or otherwise that are portrayed in them. Character theories are often based on stereotypes, and the different characteristics that make them up can either be used for positive or negatives purposes