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Math Help - Center of endomorphism algebra

  1. #1
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    Center of endomorphism algebra

    If I have an R-algebra A where R is a ring, why the center of the endomorphism algebra E_{A}(A) is the algebra of endomorphism with coefficient in the enveloping algebra A* \otimes A:

    Z(E_{A}(A))=E_{A* \otimes A}(A) ?
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  2. #2
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    Quote Originally Posted by yavanna87 View Post
    If I have an R-algebra A where R is a ring, why the center of the endomorphism algebra E_{A}(A) is the algebra of endomorphism with coefficient in the enveloping algebra A* \otimes A:

    Z(E_{A}(A))=E_{A* \otimes A}(A) ?
    well, End_A(A) \cong A and so you basically want to prove that Z(A) \cong End_{A^* \otimes_R A}(A). this is a special case of a more general problem. for a solution to the general case see this theorem in my blog. the notation C_A(B) means the centralizer of B in A.
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  3. #3
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    Thank you very much, i was trying to do that with the left regular representation right now, so I was on the right path!
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