Title: Solvable Lie algebras, Lie groups and polynomial structures
Authors: Dekimpe, Karel # ×
Issue Date: Apr-2000
Publisher: Kluwer academic publ
Series Title: Compositio mathematica vol:121 issue:2 pages:183-204
Abstract: In this paper, we study polynomial structures by starting on the Lie algebra level, then passing 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 nilpotent subalgebras. Using this result, we construct, for any simply connected, connected solvable Lie group G of dim n, a simply transitive action on R-n which is polynomial and of degree less than or equal to n(3). Finally, we show the existence of a polynomial structure on any polycyclic-by-finite group Gamma, which is of degree less than or equal to h(Gamma)(3) on almost the entire group (h (Gamma) being the Hirsch length of Gamma).
ISSN: 0010-437X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Mathematics, Campus Kulak Kortrijk
× corresponding author
# (joint) last author

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