5-dimensional indecomposable contact Lie algebras as double extensions

Abstract

In this work we shall show that a suitable double extension of a finite dimensional indecomposable contact Lie algebra is a contact Lie algebra again. In particular, with exception of the family of 5-dimensional indecomposable contact solvable Lie algebras A 5 , 35 , any 5-dimensional indecomposable contact solvable Lie algebra can be obtained as a double extension of a 3-dimensional Lie algebra. The family A 5 , 35 can be generalized to a family of ( 4 n + 1 ) -dimensional indecomposable contact solvable Lie algebras that cannot be obtained neither as a suspension of a symplectic Lie algebra of codimension 1 or as a double extension of a contact Lie subalgebra of codimension 2.