The description of dendriform algebra structures on two-dimensional complex space (Q2889953)

A dendriform algebra is an algebra with two multiplications \(\prec\) and \(\succ\) satisfying three axioms which guarantee that the multiplication \(x\ast y=x\prec y+x\succ y\) is associative. In the paper under review the authors classify all two-dimensional complex dendriform algebras. There are twelve isomorphism classes. One of the classes depends on one parameter and each of the other eleven classes consists of a single algebra. In order to obtain their classification the authors establish some properties of nilpotent dendriform algebras which are of independent interest.