Finite solvable groups with a rational skew-field of noncommutative real rational invariants

Podlogar, Gregor (author)

We consider Noether’s problem on the noncommutative rational functions invariant under a linear action of a finite group. For abelian groups the invariant skew-fields are always rational, for solvable group they are rational if the action is well-behaved – given by a so-called complete representation. We determine the groups that admit such representations and call them totally pseudo-unramified. We show that for a solvable group the invariant skew-field is finitely generated. Finally we study totally pseudo-unramified groups and classify totally pseudo-unramified $p$-groups of rank at most $5$.

• Language: English
• Keywords: Clifford theory, multiplicity free restrictions, noncommutative Noether’s problem, noncommutative rational invariant, totally unramified groups
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: Str. 2268-2292
• Numbering: Vol. 51, no. 6
• PID: 20.500.12556/RUL-159177
• UDC: 512
• ISSN on article: 0092-7872
• DOI: 10.1080/00927872.2022.2156526
• COBISS.SI-ID: 200488195
• Publication date in RUL: 02.07.2024

Record is a part of a journal

• Title: Communications in algebra
• Shortened title: Commun. algebra
• Publisher: Taylor & Francis
• ISSN: 0092-7872
• COBISS.SI-ID: 25249792

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.