Category:Regular Representations
Jump to navigation
Jump to search
This category contains results about Regular Representations.
Definitions specific to this category can be found in Definitions/Regular Representations.
Let $\struct {S, \circ}$ be a magma.
Left Regular Representation
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 $a$.
Right Regular Representation
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 $a$.
Subcategories
This category has the following 3 subcategories, out of 3 total.
L
- Left Regular Representation (empty)
Pages in category "Regular Representations"
The following 23 pages are in this category, out of 23 total.
C
L
R
- Regular Representation of Invertible Element is Permutation
- Regular Representation on Subgroup is Bijection to Coset
- Regular Representation wrt Cancellable Element on Finite Semigroup is Bijection
- Regular Representations in Group are Permutations
- Regular Representations in Semigroup are Permutations then Structure is Group
- Regular Representations of Subset Product
- Regular Representations wrt Element are Permutations then Element is Invertible
- Right and Left Regular Representations in Topological Group are Homeomorphisms
- Right Cancellable iff Right Regular Representation Injective
- Right Regular Representation by Inverse is Transitive Group Action
- Right Regular Representation of 0 is Bijection in B-Algebra
- Right Regular Representation of Subset Product
- Right Regular Representation wrt Right Cancellable Element on Finite Semigroup is Bijection