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Other Situations Involving Group Matrices

  • Kenneth W. Johnson
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2233)

Abstract

This chapter sketches various situations in which the tools described in this book have appeared. They are:
  1. 1.

    The characterization of those class functions on a group which are group characters.

     
  2. 2.

    The use of group matrices in the theory of group rings.

     
  3. 3.

    The application of group matrices to the theory of cogrowth of groups.

     
  4. 4.

    Work of Poincaré on differential equations.

     
  5. 5.

    The connection between factors of the group determinant and Chern classes.

     
  6. 6.

    The appearance of the group matrix as a Gram matrix for tight frames with a symmetry group, which have appeared in the theory of wavelets.

     
  7. 7.

    The theory of 3-manifolds.

     
  8. 8.

    Control theory and electrical engineering.

     
  9. 9.

    The algebra defined by considering the k-classes under multiplication.

     

Notes

Acknowledgments

The author would like to acknowledge the uses of GAP [115, 118] and the related package LOOPs [222] in calculations for the book.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kenneth W. Johnson
    • 1
  1. 1.Department of MathematicsPennsylvania State UniversityAbingtonUSA

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