On nilpotent Leibniz algebras, Lie biderivations and related topics

This thesis classifies two-step nilpotent Leibniz algebras, with a specific emphasis on the real and complex cases of Heisenberg Leibniz algebras. It demonstrates a global integration property for nilpotent real Leibniz algebras, explores integra- tion in specific scenarios and solves the coquecigrue problem by integrating into a Lie rack. It investigates Lie algebras of derivations in two-step nilpotent algebras and describes isotopism classes of nilpotent Leibniz algebras and introduces new invariants. Biderivations of complete Lie algebras are also described, with attention given to both symmetric and skew-symmetric cases. Furthermore, it provides isomorphism results for non-nilpotent non-Lie Leibniz algebras with a one-dimensional derived subalgebra.