Definition:Regular Representations/Left Regular Representation

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Let $\struct {S, \circ}$ be a magma.

The mapping $\lambda_a: S \to S$ is defined as:

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

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

Also known as

For the left regular representation, some sources use a hyphen: left-regular representation.

Some sources refer to the left regular representation as left multiplication.

Also defined as

Some treatments of abstract algebra and group theory define the regular representations for semigroups.

Some define it only for groups.

Also see

  • Results about regular representations can be found here.