CENTRAL EXTENSIONS OF FINITE-DIMENSIONAL NILPOTENT LEIBNIZ ALGEBRAS OF SMALL DIMENSION

This paper investigates one-dimensional central extensions of small-dimensional nonnilpotent filiform Leibniz algebras. In particular, we consider the algebras F1(0,0,0,1)  and F2(0,1,0,0),constructing their multiplication tables and analyzing their automorphisms. Using the structure of 2-cocycles and the corresponding cohomology spaces, we classify all possible central extensions. By examining the action of the automorphism group on the second cohomology, we determine the complete set of nonisomorphic one-dimensional central extensions of these algebras. The results provide a deeper understanding of the structure of filiform Leibniz algebras and contribute to the broader classification of their central extensions