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【本科生沙龙】分析与代数讨论班 第十四期
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       #Math101 Session 14

       Time:May 16, 2022, 13:30--15:30

       Location:434 Qi Xiang Building, Chang'an Campus

       Speaker:Mr.Zhang,Zhenhao (Class of 2024)

       Title:A proof of Skolem-Noether theorem for matrixalgebras

       Abstract:Given an integern, the ring of real square matrices of ordernis an algebra over the field of real numbers under matrix addition and matrix multiplication. Any automorphism of this matrix algebra is conjugation by some invertible matrixAof the same order.This is a special case of the Skolem-Noether theorem, a fundamental result in the theoryof central simple algebras and representation theory. In this talk, we will provide an elementary proof of the theorem above, which is entirely constructive andgives the matrixAexplicitly. We also note that the conclusion holds for matrix algebras over a general fieldKand correspondingK-automorphisms.