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Inverses of Cartan matrices of Lie algebras and Lie superalgebras
Dimitry Leites, Oleksandr Lozhechnyk
The inverses of indecomposable Cartan matrices are computed for finite-dimension\-al Lie algebras and Lie superalgebras over fields of any characteristic, and for hyperbolic (almos…
The roots of exceptional modular Lie superalgebras with Cartan matrix
Sofiane Bouarroudj, Dimitry Leites, Alexander Lozhechnyk +1
For each of the exceptional Lie superalgebras with indecomposable Cartan matrix, we give the explicit list of its roots of and the corresponding Chevalley basis for one of the ineq…
Computer-aided study of double extensions of restricted Lie superalgebras preserving the non-degenerate closed 2-forms in characteristic 2
Sofiane Bouarroudj, Dimitry Leites, Jin Shang
A Lie (super)algebra with a non-degenerate invariant symmetric bilinear form is called a nis-(super)algebra. The double extension of a nis-(super)algebra $\mathf…