Solvable Lie Algebras, Lie Groups andPolynomial Structures |
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Authors: | KAREL Dekimpe |
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Affiliation: | (1) Katholieke Universiteit Leuven Campus Kortrijk, B-8500 Kortrijk, Belgium |
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Abstract: | In this paper, we study polynomial structures by starting on the Lie algebra level, thenpassing to Lie groups to finally arrive at the polycyclic-by-finite group level. To be more precise,we first show how a general solvable Lie algebra can be decomposed into a sum of two nilpotentsubalgebras. Using this result, we construct, for any simply connected, connected solvable Lie groupG of dim n, a simply transitive action on Rn which is polynomial and of degree n3. Finally, we show the existence of a polynomial structure on any polycyclic-by-finite group , which is of degree h()3 on almost the entire group (h () being the Hirsch length of ). |
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