  In this paper, we extend the concept of Lie superalgebras to a more
generalized framework called Super-Lie superalgebras. In addition, they seem to
be exploring various supergeneralizations of other algebraic structures, such
as Super-associative, left (right) Super-Leibniz, and
Super-left(right)-symmetric superalgebras, then we give some examples and
related fundamental results. The notion of Rota-Baxter operators with any
parity on the Super-Lie superalgebras is given. Moreover, we study a
representations of Super-Lie superalgebras and its associate dual
representations. The notion of derivations of Super-Lie superalgebras is
introduced thus we show that the converse of a bijective derivation defines a
Rota-Baxter operator. Finally, we give a generalization of the Super-Lie
superalgebras and some other structures in the ternary case which we supported
this with some examples and interesting results.
