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

Podlogar, Gregor (avtor)

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 $5$.

• Jezik: Angleški jezik
• Ključne besede: Clifford theory, multiplicity free restrictions, noncommutative Noether’s problem, noncommutative rational invariant, totally unramified groups
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2023
• Št. strani: Str. 2268-2292
• Številčenje: Vol. 51, no. 6
• PID: 20.500.12556/RUL-159177
• UDK: 512
• ISSN pri članku: 0092-7872
• DOI: 10.1080/00927872.2022.2156526
• COBISS.SI-ID: 200488195
• Datum objave v RUL: 02.07.2024

Gradivo je del revije

• Naslov: Communications in algebra
• Skrajšan naslov: Commun. algebra
• Založnik: Taylor & Francis
• ISSN: 0092-7872
• COBISS.SI-ID: 25249792

Licence

• Licenca: CC BY-NC-ND 4.0, Creative Commons Priznanje avtorstva-Nekomercialno-Brez predelav 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc-nd/4.0/deed.sl
• Opis: Najbolj omejujoča licenca Creative Commons. Uporabniki lahko prenesejo in delijo delo v nekomercialne namene in ga ne smejo uporabiti za nobene druge namene.