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Noncommutative rational functions invariant under the action of a finite solvable group
Journal of Mathematical Analysis and Applications ( IF 1.3 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.jmaa.2020.124341
Igor Klep , James Eldred Pascoe , Gregor Podlogar , Jurij Volčič

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.

中文翻译:

有限可解群作用下不变的非交换有理函数

本文描述了有限可解群在 $d$ 生成器中的自由斜场上的线性作用的不变斜场的结构。这些不变的偏斜场总是有限生成的,这与自由代数情况形成对比。对于具有良好表示理论的阿贝尔群或可解群 $G$,表明不变斜场在 $|G|(d-1)+1$ 生成器上是自由的。最后,根据不变量的平方和给出了不变有理函数的正性证明。
更新日期:2020-10-01
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