Some remarks on solvable Lie superalgebras
The authors investigate the classification problem for (solvable) Lie superalgebras. In particular, they settle the case when the even part is a solvable Lie algebra \(\mathfrak g\) and the odd part is a two-dimensional representation of \(\mathfrak g\). They also point out which of these solvable superalgebras fail to be completely solvable; this is the exception, not the rule. One technique used is to see how, once one fixes some Lie algebra \(\mathfrak g\), the superalgebra changes as one varies the odd part in the space of representations of \(\mathfrak g\) (of a fixed dimension). Especially, the authors determine the possibilities when the representation is semisimple. In addition, it is shown that if the bilinear form on the odd part of a Lie superalgebra is non-degenerate then the microlocalisation of the enveloping algebra at the symmetrisation of determinant of the matrix of the bilinear form is a maximal order of finite global dimension.
scientific article; zbMATH DE number 762331
scientific article