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A complete classification of two-dimensional algebras over algebraically closed fields is provided.

Application of abelian holonomy formalism to the elementary theory of numbers J. Math. Phys. 53, 052303 (2012) Asymptotic behavior of the Verblunsky coefficients for the OPUC with a varying weight J. Math. Phys. 53, 043510 (2012) Construction of time-dependent dynamical invariants: A new approach J. Math. Phys. 53, 042104 (2012) Essential self-adjointness of Wick squares in quasi-free Hadamard representations on curved spacetimes Abstract. The aim of this paper is to complete the classification of three-dimensional complex Leibniz algebras. The description of isomorphism classes of three-dimensional complex Leibniz algebras has been given by Ayupov and Omirov in 1999. However, we found that this list has a little redundancy. In this paper we apply a method which is more elegant and it gives the precise list of isomorphism classes of these algebras. We compare our list with that of Ayupov-Omirov and show the corrections which should be made.

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