Generalized Characters for Glider Representations of Groups

  • Frederik CaenepeelEmail author
  • Fred Van Oystaeyen


Glider representations can be defined for a finite algebra filtration FKG determined by a chain of subgroups 1 ⊂ G1 ⊂… ⊂ Gd = G. In this paper we develop the generalized character theory for such glider representations. We give the generalization of Artin’s theorem and define a generalized inproduct. For finite abelian groups G with chain 1 ⊂ G, we explicitly calculate the generalized character ring and compute its semisimple quotient. The papers ends with a discussion of the quaternion group as a first non-abelian example.


Groups Glider representations Character theory 

Mathematics Subject Classification (2010)



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The first author expresses his gratitude to Geoffrey Janssens and Eric Jespers for fruitful discussions on the calculation of the Jacobson radical and the primitive central idempotents of semigroup algebras appearing in the theory of glider representations.


  1. 1.
    Caenepeel, F., Van Oystaeyen, F.: Clifford theory for glider representations. Algebr. Represent. Theory 19(6), 1477–1493 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Caenepeel, F., Van Oystaeyen, F.: Glider representations of group algebra filtrations of nilpotent groups. Algebr. Represent. Theory,
  3. 3.
    El Baroudy, M., Van Oystaeyen, F.: Fragments with finiteness condtions in particular over group rings. Comm. Algebra 28(1), 321–336 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    James, G., Liebeck, M.: Representations and Characters of Groups, 2nd edn. Cambridge University Press, New York (2001). viii+ 458 pp.CrossRefzbMATHGoogle Scholar
  5. 5.
    Jespers, E., Leal, G., Paques, A.: Central idempotents in the rational group algebra of a finite nilpotent group. J. Algebra Appl. 2(1), 57–62 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Nawal, S., Van Oystaeyen, F.: An introduction of fragmented structures over filtered rings. Comm. Algebra 23, 975–993 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Okniński, J.: Semigroup Algebras. Marcel Dekker (1998)Google Scholar
  8. 8.
    Serre, J.-P.: Linear Representations of Finite Groups, Translated from the second French edition by Leonard L. Scott, Graduate Texts in Mathematics, vol. 42. Springer, New York (1977). x + 170 pp.Google Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AntwerpAntwerpBelgium
  2. 2.Shanghai Center for Mathematical SciencesFudan UniversityShanghaiChina

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