Noncommutative rational functions invariant under the action of a finite solvable group

Igor Klep, James Eldred Pascoe, Gregor Podlogar, Jurij Volčič

Research output: Contribution to journalArticlepeer-review

Abstract

This paper describes the structure of invariant skew fields for linear actions of finite solvable groups on free skew fields in d generators. These invariant skew fields are always finitely generated, which contrasts with the free algebra case. For abelian groups or solvable groups G with a well-behaved representation theory it is shown that the invariant skew fields are free on |G|(d−1)+1 generators. Finally, positivity certificates for invariant rational functions in terms of sums of squares of invariants are presented.

Original languageEnglish
Article number124341
JournalJournal of Mathematical Analysis and Applications
Volume490
Issue number2
DOIs
StatePublished - 15 Oct 2020
Externally publishedYes

Keywords

  • Group representation
  • Invariant field
  • Noncommutative rational function
  • Positive rational function

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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