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Nonsplit extensions of modular Lie algebras of rank 2. (English) Zbl 0997.17007
It is well-known that contrary to characteristic zero the second Whitehead lemma does not hold for finite-dimensional semisimple Lie algebras over fields of prime characteristic. More generally, every finite-dimensional modular Lie algebra has finite-dimensional (and thus irreducible) modules with nonzero second cohomology. Since there are only finitely many isomorphism classes of irreducible modules with this property, a complete list of the second cohomology groups with irreducible coefficients for any finite-dimensional Lie algebra over a field of prime characteristic can be considered as a modular substitute for the second Whitehead lemma. In the paper under review the authors give such a list for the classical simple Lie algebras of rank 2 over algebraically closed fields of characteristic \(p\) larger than the Coxeter number.
MSC:
17B20 Simple, semisimple, reductive (super)algebras
17B50 Modular Lie (super)algebras
17B25 Exceptional (super)algebras
17B56 Cohomology of Lie (super)algebras
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