Cohomology and deformation for dendriform algebra with a derivation

Abstract

Dendriform algebras can be regarded as associative algebras whose product is decomposed into two operations satisfying some laws of dendriform algebra, which together form the associative law of the undecomposed associative algebra. We introduce a cohomology theory for dendriform algebras equipped with derivations and show the deformation theory is controlled by the cohomology and the collection of equivalence classes of abelian extensions is given by the second cohomology.