JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (2): 44-50.doi: 10.6040/j.issn.1671-9352.0.2021.725

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Maschke theorem for the Grothendieck algebra of dihedral group

CAO Liu-feng   

  1. School of Mathematics, Yangzhou University, Yangzhou 225002, Jiangsu, China
  • Published:2023-02-12

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Abstract: Let F be an algebraically closed field with characteristic 0, and n=2N+1 be any odd number, we calculating the Casimir number of the Grothendieck ring r(FDn) of the dihedral group Dn equals 2n2 explicitly. Furthermore, we give the Maschke theorem for the corresponding Grothendieck algebra of dihedral group.

Key words: dihedral group, Grothendieck ring, Casimir number, Jacobson radical

CLC Number: 

  • O153.3
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