Definition:Regular Representations/Left Regular Representation

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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 defined as

Some treatments of abstract algebra and group theory define this construct for semigroups.

Some define it only for groups.


Also see

  • Results about regular representations can be found here.


Sources