  The aim of this work is to introduce representations of BiHom-left-symmetric
algebras. and develop its cohomology theory. As applications, we study linear
deformations of BiHom-left-symmetric algebras, which are characterized by its
second cohomology group with the coefficients in the adjoint representation.
The notion of a Nijenhuis operator on a BiHom-left-symmetric algebra is
introduced. We will prove that it can generate trivial linear deformations of a
BiHom-left-symmetric algebra.
