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## Ask for general method to realize an finite associate algebra as matrix algebra…

Every n-dimensional associate algebra can realize as matrix subalgebra of $M_{n^2}(C)$.Consider the base field is the complex number field. My questions is what resource I can consult to archive this aim.

1.realize a finite abstract group as a matrix group.

2.realize n-dimensional associate algebra as matrix subalgebra of $M_{n^2}(C)$.

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You want the subject known as representation theory. There is a vast literature here. – Qiaochu Yuan Aug 26 2011 at 3:21
It's not clear whether you just want some realization as in 1. and 2. or whether you want general information about such realizations. In the former case, for 1., use the proof of Cayley's theorem to represent your group by permutations and then write these as permutation matrices, and for 2. choose a linear basis for your algebra and represent each element $a$ by the matrix (under this basis) of the linear operation of multiplication by $a$. In the latter case, I agree with Qiaochu. – Andreas Blass Aug 26 2011 at 3:50
Thank you very much! It seems a stupid question.I know how to solve my problem now. – X--- Aug 28 2011 at 11:06