This paper is devoted to show and explain some applications of Lie theory to solve some problems in Economics and Mathematical Finance. So we put forward and discuss mathematical aspects and approaches for several economic problems which have been previously considered in the literature. Besides we also show our advances on this topic, mentioning some open problems for future research.
In this paper, we study the varieties of nilpotent Lie superalgebras of dimension {\leq 5}.
We provide the algebraic classification of these superalgebras and obtain the irreducible components in every variety.
As a byproduct, we construct rigid nilpotent Lie superalgebras of arbitrary dimension.
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