Definition:Regular Representations/Left Regular Representation
From ProofWiki
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 $a$.
Sources
- Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 8$
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 35$
