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Symmetries of differential behaviors and finite group actions on free modules over a polynomial ring. (English) Zbl 0802.93029
Summary: We study finite group symmetries of differential behaviors (i.e., kernels of linear constant coefficient partial differential operators). They lead us to study the actions of a finite group on free modules over a polynomial ring. We establish algebraic results which are then used to obtain canonical differential representations of symmetric differential behaviors.

MSC:
93C05 Linear systems in control theory
37-XX Dynamical systems and ergodic theory
13N10 Commutative rings of differential operators and their modules
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