Invariants for finite group actions on skew fields
Revisiting Fundamental Problems Workshop: Infinite-Dimensional Division Algebras - Algebraicity and Freeness December 01, 2025 - December 05, 2025
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
Invariants for finite group actions on skew fields
In this talk I will discuss some recent results on invariants of group actions on skew fields in joint work with Jurij Volcic: Suppose that G is a finite group acting on a finitely generated skew field M. If L is the set of invariants then L is also a finitely generated skew field. I will describe an algorithm to obtain a set of generators. If M is the free skew field with m generators, and the group action is linear, then L is free with |G|(m-1)+1 generators. However, if the action is non-linear, then the invariant subfield L may not be free.
Invariants for finite group actions on skew fields
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