What is isomorphic representation?
Isomorphic representations are, for practical purposes, “the same”; they provide the same information about the group or algebra being represented. Representation theory therefore seeks to classify representations up to isomorphism.
Who discovered representation theory?
Abstract. Representation theory was created by Frobenius about 100 years ago. We describe the background that led to the problem which motivated Frobenius to define characters of a finite group and show how representation theory solves the problem.
What is the point of representation theory?
“Roughly speaking, representation theory investigates how algebraic systems can act on vector spaces. When the vector spaces are finite-dimensional this allows one to explicitly express the elements of the algebraic system by matrices, hence one can exploit linear algebra to study ‘abstract’ algebraic systems.
What is a representation analysis?
Representation always involves a certain degree of abstraction—that is, the taking away of one characteristic or more of the original. The representation is, of course, not a visual one; it is representation through language. …
What are the different types of representations?
Models of representation refer to ways in which elected officials behave in representative democracies. There are three main types: delegate, trustee, and politico.
What is meant by equivalent representations?
Two representations of an algebra are sometimes called equivalent, or isomorphic, if their kernels coincide; two representations of a topological group are called equivalent if the induced representations of some group algebra of this group are isomorphic. …
Are representations linear?
A linear representation is a representation on a category of vector spaces or similar (Vect, Mod, etc.) One sometimes considers representations on objects other than linear spaces (such as permutation representations) but often these are called not representations but actions.
What is social representation theory?
Social representations theory is a “theory of social knowledge” specifically concerned with how individuals, groups, and communities collectively make sense of socially relevant or problematic issues, ideas, and practices (Marková 2008:483).
How are representations constructed?
Representations are created through a process of selection, omission and construction. These decisions all influence the meaning that you create and how audiences will read your representation. The word ‘code’ refers to any system of signs that are used to communicate meaning.
What are the four types of representations?
“Can someone please explain the four models of representation (delegate, partisan, trustee and mirror).
What are the 3 types of representation?