The aim of this paper is to extend
to ternary algebras the classical theory of formal deformations of algebras
introduced by Gerstenhaber. The associativity of ternary algebras is available in two forms, totally associative case or partially associative case. To any
partially associative algebra corresponds by anti-commutation a ternary Lie
algebra. In this work, we summarize the principal definitions and properties as
well as classification in dimension 2 of these algebras. Then we focuss ourselves
on the partially associative ternary algebras, we construct the first groups of
a cohomolgy adapted to formal deformations and then we work out a theory of
formal deformation in a way similar to the binary algebras.
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