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Math Help - regular representations

  1. #1
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    regular representations

    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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  2. #2
    ynj
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    Quote Originally Posted by alexandrabel90 View Post
    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.
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  3. #3
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    thank you!

    but when is the left or right regular representation used?
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  4. #4
    ynj
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    Quote Originally Posted by alexandrabel90 View Post
    thank you!

    but when is the left or right regular representation used?
    To prove that every group is isomorphic to a permutation group.
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  5. #5
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    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?
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  6. #6
    ynj
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    Quote Originally Posted by alexandrabel90 View Post
    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_aform 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.
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