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arXiv · 1909.08043

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

Igor Klep·James Eldred Pascoe·Gregor Podlogar·Jurij Volčič
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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.

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Igor Klep, James Eldred Pascoe, Gregor Podlogar, Jurij Volčič. 2019-09-17. Noncommutative rational functions invariant under the action of a finite solvable group. https://doi.org/10.1016/j.jmaa.2020.124341

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