Definition:Regular Representations/Left Regular Representation

Definition
Let $\left ({S, \circ}\right)$ be a semigroup. The mapping $\lambda_a: S \to S$ is defined as:


 * $\forall a \in S: \lambda_a \left({x}\right) = a \circ x$

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