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

thanks!

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- Sep 1st 2009, 03:34 AMalexandrabel90regular representations
Can someone explain what does right and left regular representations of a group G mean and the purpose of it?

thanks! - Sep 1st 2009, 03:57 AMynj
- Sep 1st 2009, 05:03 AMalexandrabel90
thank you!

but when is the left or right regular representation used? - Sep 1st 2009, 05:04 AMynj
- Sep 1st 2009, 05:12 AMalexandrabel90
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?

- Sep 1st 2009, 05:39 AMynj
no,it actually means that each $\displaystyle \lambda_a$ is a permutation on $\displaystyle G$, and all these $\displaystyle \lambda_a$form a group which is isomorphic to $\displaystyle G$.

All the left regular representations of G form a group that is isomorphic to G, so does the right regular representations.