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The aim of this work is to give necessary and sufficient conditions to extend an LSA structure on a Lie algebrato a Lie algebrathat either containsas a subalgebra, or is a central extension of it. We also study conditions under which a Lie algebra together with an LSA structure admit a Frobenius or a contact form. Furthermore, we describe the properties of the Reeb vector associated with the codimension one contact ideal with respect to the LSA structure on the Frobenius Lie algebra.

Left-symmetric algebra structures on contact Lie algebras