The Lie algebra g_{-1}^B from gl_{m|n} via derived bracket is classified up to isomorphism by rank(B)=r and the set {m,n}, with Levi factor sl(r).
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Classification of Lie algebras constructed from $\mathfrak{gl}_{m|n}$ via Derived Bracket
The Lie algebra g_{-1}^B from gl_{m|n} via derived bracket is classified up to isomorphism by rank(B)=r and the set {m,n}, with Levi factor sl(r).