1. ## regular representations

Can someone explain what does right and left regular representations of a group G mean and the purpose of it?

thanks!

2. Originally Posted by alexandrabel90
Can someone explain what does right and left regular representations of a group G mean and the purpose of it?

thanks!
Left regular representation means a map $\lambda_a:G\rightarrow G,\lambda_a(g)=ag$.

3. thank you!

but when is the left or right regular representation used?

4. Originally Posted by alexandrabel90
thank you!

but when is the left or right regular representation used?
To prove that every group is isomorphic to a permutation group.

5. sorry, im new to this topic so im rather lost. Those that mean that is there is a left and right regular representation for a group G, it is isomorphic? or what?

6. Originally Posted by alexandrabel90
sorry, im new to this topic so im rather lost. Those that mean that is there is a left and right regular representation for a group G, it is isomorphic? or what?
no,it actually means that each $\lambda_a$ is a permutation on $G$, and all these $\lambda_a$form a group which is isomorphic to $G$.
All the left regular representations of G form a group that is isomorphic to G, so does the right regular representations.