152 research outputs found
Derivations and central extensions of symmetric modular Lie algebras and superalgebras
Over algebraically closed fields of positive characteristic, for simple Lie
(super)algebras, and certain Lie (super)algebras close to simple ones, with
symmetric root systems (such that for each root, there is minus it of the same
multiplicity) and of ranks most needed in an approach to the classification of
simple vectorial Lie superalgebras, we list the outer derivations and
nontrivial central extensions. When the answer is clear for the infinite
series, it is given for any rank.
We also list the outer derivations and nontrivial central extensions of one
series of nonsymmetric, namely, periplectic Lie superalgebras (of any rank)
preserving the nondegenerate supersymmetric odd bilinear forms, and of the Lie
algebras obtained from periplectic Lie superalgebras by desuperization when the
characteristic of the ground field is equal to 2.
We also list the outer derivations and nontrivial central extensions of an
analog of the rank 2 exceptional Lie algebra discovered by Shen Guangyu.
Several results are counterintuitive.Comment: 36 page
- …