Definition:Regular Representations/Left Regular Representation

Definition
Let $\struct {S, \circ}$ be a magma. The mapping $\lambda_a: S \to S$ is defined as:


 * $\forall a \in S: \map {\lambda_a} x = a \circ x$

This is known as the left regular representation of $\struct {S, \circ}$ with respect to $a$.

Also known as
Some sources use a hyphen: left-regular representation.

Also see

 * Definition:Right Regular Representation


 * Left Regular Representation of Subset Product


 * Regular Representations of Invertible Elements are Permutations
 * Regular Representations in Group are Permutations