Shujuan Wang, Zhaoxin Li
Published 2022-06-16Version 1
Over a field of characteristic $p>2,$ the first cohomology of the 3-dimensional simple Lie algebra $\frak{sl}(2)$ with coefficients in all simple modules is determined, which implies Whitehead's first lemma is not true in prime characteristic. As applications, derivations and 2-local derivations of $\frak{sl}(2)$ on any simple module are also be characterized.
Casimir elements associated with Levi subalgebras of simple Lie algebras and their applications
Dualities for root systems with automorphisms and applications to non-split groups
Correspondences between affine Hecke algebras and applications
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