Darboux families and the classification of real four-dimensional indecomposable coboundary Lie bialgebras

11 Feb 2021 J. de Lucas D. Wysocki

This work introduces a new concept, the so-called Darboux family, which is employed to determine, to analyse geometrically, and to classify up to Lie algebra automorphisms, in a relatively easy manner, coboundary Liebialgebras on real four-dimensional indecomposable Lie algebras. The Darboux family notion can be consideredas a generalisation of the Darboux polynomial for a vector field... (read more)

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  • MATHEMATICAL PHYSICS
  • DIFFERENTIAL GEOMETRY
  • MATHEMATICAL PHYSICS
  • QUANTUM ALGEBRA