HYPER COMPLEX STRUCTURES APPEARED IN THE PHYSICAL THEORY OF SUPER SYMMETRY HAS BEEN INTERESTED IN PHYSICS AND MATHEMATICS. SUPER SYMMETRY CAN BE DESCRIBED BY LIE SUPER ALGEBRAS USING COMMUTING AND ANTI-COMMUTING VARIABLES. RECENTLY, THE COMPLEX STRUCTURES ON LIE SUPER ALGEBRAS AND INVARIANT HYPER COMPLEX STRUCTURES ON LIE ALGEBRAS HAVE BEEN INTERESTED IN [2, 3, 4, 6, 8, 10, 11, 14]. THE GOAL OF THIS TALK PAPER IS TO EXTEND THE HYPER COMPLEX STRUCTURE NOTION TO LIE SUPER ALGEBRAS WITH EMPHASIZING ON SOLVABILITY AND THE DIMENSION OF THE DERIVATION OF EVEN PART OF A LIE SUPER ALGEBRA.