  In this paper, we introduced the notion of Hom-Lie antialgebras. The
representations and cohomology theory of Hom-Lie antialgebras are investigated.
We prove that the equivalent classes of abelian extensions of Hom-Lie
antialgebras are in one-to-one correspondence to elements of the second
cohomology group. We also prove that 1-parameter infinitesimal deformation of a
Hom-Lie antialgebra are characterized by 2-cocycles of this Hom-Lie antialgebra
with adjoint representation in itself. The notion of Nijenhuis operators of
Hom-Lie antialgebra is introduced to describe trivial deformations.
