The Dixmier map for nilpotent super Lie algebras
The author extends the classical Dixmier map for nilpotent Lie algebras, to the setting of nilpotent super Lie algebras. In particular, using the existence of polarizations also in this case, he proves that if \(\mathfrak{g}=\mathfrak{g}_0\oplus\mathfrak{g}_1\) is a nilpotent super Lie algebra and \(\mathrm{Ad}_0\) is the adjoint group of \(\mathfrak{g}_0\), then there exists a bijective map \(I:\mathfrak{g}^\ast_0/\mathrm{Ad}_0\longrightarrow\mathrm{Prim}(U(\mathfrak{g}))\) sending an equivalence class \([\lambda]\) to a primitive ideal \(I(\lambda)\) of \(U(\mathfrak{g})\). This map coincides with the ordinary Dixmier map.
scientific article; zbMATH DE number 6065243
scientific article