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Moduli spaces of low dimensional Lie superalgebras
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In this paper, we study moduli spaces of low dimensional complex Lie superalgebras. We discover a similar pattern for the structure of these moduli spaces as we observed for ordinary Lie algebras, namely, that there is a stratification of the moduli space by projective orbifolds. The moduli spaces consist of some families as well as some singleton elements. The different strata are linked by jump deformations, which gives a uniques manner of decomposing the moduli space which is consistent with deformation theory.
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Varieties of Nilpotent Lie Superalgebras of dimension $\leq 5$
The nilpotent Lie superalgebras of dimension at most five are classified, their degenerations and irreducible components are found, and rigid nilpotent Lie superalgebras are constructed in every dimension.
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