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Lie algebras with finite-dimensional polynomial centralizer |
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| Authors: | Giuseppe Gaeta Sebastian Walcher |
| Affiliation: | a Dipartimento di Matematica, Universitá di Milano, via Saldini 50, 20133 Milano, Italy b Dipartimento di Fisica, Universitá di Roma, P.le A. Moro 5, 00185 Roma, Italy c Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen, Germany d Institut für Biomathematik und Biometrie, GSF-Forschungszentrum, Ingolstädter Landstr. 1, 85764 Neuherberg, Germany |
| Abstract: | We give criteria for finite or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite-dimensional scenario some applications to normal forms and to certain equations with fundamental solutions are presented. |
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