Trivial linear representation: Difference between revisions

Revision as of 16:29, 2 November 2023

This article gives a basic definition in the following area: linear representation theory
View other basic definitions in linear representation theory |View terms related to linear representation theory |View facts related to linear representation theory

Definition

Let $G$ be a group, and $K$ be a field.

Then the map $ρ : G \to G L_{1} (K)$ sending each element of $G$ to the $1 \times 1$ identity matrix is a linear representation. It is called the trivial representation.

Character

The character of this representation is $1$ on all elements of the group.

Revision as of 16:28, 2 November 2023 (view source) R-a-jones (talk \| contribs) (Created page with "==Definition== Let <math>G</math> be a group, and <math>K</math> be a field. Then the map <math>\rho: G \to GL_1(K)</math> sending each element of <math>G</math> to...")		Revision as of 16:29, 2 November 2023 (view source) R-a-jones (talk \| contribs) No edit summary Newer edit →
Line 1:		Line 1:
			{{basicdef in\|linear representation theory}}

	==Definition==		==Definition==