Norm Forms and Group Determinant Factors

Kenneth W. Johnson

Research output: Chapter in Book/Report/Conference proceedingChapter


The usual approach to group representations in modern texts is via the theory of algebras and modules. This chapter is based on a less well-known constructive approach to the theory of algebras which uses the generalization to noncommutative algebras of a (multiplicative) norm, which can be applied to obtain results on group determinants. This continues a line of research which goes back to Frobenius. Significant results which have not been translated into modern abstract accounts are to be found there. An essential result is that given a norm-type form on an algebra with suitable assumptions, the form can be constructed rationally from the first three coefficients of its “characteristic equation”. This, applied to the group determinant, shows that the 1-, 2- and 3-characters determine a group.

Original languageEnglish (US)
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Number of pages26
StatePublished - Jan 1 2019

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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