Complete Classification of Two-Dimensional Algebras

A complete classification of two-dimensional algebras over algebraically closed fields is providedComment: A type-mistake in $A_{3,2}(\mathbf{c})$ case, page 7, is correcte

The automorphism groups and derivation algebras of two-dimensional algebras

The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.Comment: A type-mistake in $A_{3,2}(\mathbf{c})$ case, page 4, and its consequences are are correcte