Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE KERNELS OF THE LINEAR MAPS OF FINITE GROUP ALGEBRAS

  • Dan Yan (MOE-LCSM School of Mathematics and Statistics Hunan Normal University)
  • Received : 2023.01.02
  • Accepted : 2023.09.01
  • Published : 2024.01.31
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Abstract

Let G be a finite group, K a split field for G, and L a linear map from K[G] to K. In our paper, we first give sufficient and necessary conditions for Ker L and Ker L ∩ Z(K[G]), respectively, to be Mathieu-Zhao spaces for some linear maps L. Then we give equivalent conditions for Ker L to be Mathieu-Zhao spaces of K[G] in term of the degrees of irreducible representations of G over K if G is a finite Abelian group or G has a normal Sylow p-subgroup H and L are class functions of G/H. In particular, we classify all Mathieu-Zhao spaces of the finite Abelian group algebras if K is a split field for G.

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Acknowledgement

The author is very grateful to professor Wenhua Zhao for some useful suggestions. She is also grateful to the Department of Mathematics of Illinois State University, where this paper was partially finished, for hospitality during her stay as a visiting scholar. The author is very grateful to the referee for some useful suggestions and comments.

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