Maximal solvable subalgebras of Lie superalgebras \({\mathfrak {gl}}(m| n)\) and \({\mathfrak {sl}}(m| n)\)
For a Lie superalgebra \({\mathfrak g}= {\mathfrak g}_0+ {\mathfrak g}_1= {\mathfrak {sl}} (m|n)\) O. M. Sulim described all its maximal solvable subalgebras \({\mathfrak r}= {\mathfrak r}_0+ {\mathfrak r}_1\), whose even part \({\mathfrak r}_0\) is a Borel subalgebra of the Lie algebra \({\mathfrak g}_0\). In this paper a method for constructing a broader class of maximal solvable subalgebras of the Lie superalgebras \({\mathfrak {gl}} (m|n)\) and \({\mathfrak {sl}} (m|n)\) is presented where the family of Sulim's special superalgebras is obtained as a regular part of the new construction.
scientific article; zbMATH DE number 795632
scientific article