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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:490

Article

Klep, Igor¹  Pascoe, James Eldred²  Podlogar, Gregor³  Volcic, Jurij⁴ 

[1] Univ Ljubljana, Fac Math & Phys, Dept Math, Ljubljana, Slovenia

[2] Univ Florida, Dept Math, Gainesville, FL 32611 USA

[3] Inst Math Phys & Mech, Ljubljana, Slovenia

[4] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

关键词: Noncommutative rational function;    Invariant field;    Group representation;    Positive rational function;   

DOI  :  10.1016/j.jmaa.2020.124341

来源: Elsevier

【 摘 要 】

This paper describes the structure of invariant skew fields for linear actions of finite solvable groups on free skew fields in dgenerators. These invariant skew fields are always finitely generated, which contrasts with the free algebra case. For abelian groups or solvable groups Gwith a well-behaved representation theory it is shown that the invariant skew fields are free on vertical bar G vertical bar(d - 1) + 1generators. Finally, positivity certificates for invariant rational functions in terms of sums of squares of invariants are presented. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free