Definition:Regular Representations/Right Regular Representation

From ProofWiki
Jump to navigation Jump to search


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

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

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

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

Also known as

Some sources use a hyphen: right-regular representation.

However, this can be confusing: when the term right appears hyphenated in this manner, it usually has the meaning of perpendicular or orthogonal.

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.