On the third cohomology of simple SL2-modules

Abstract

The third cohomology groups of simple modules for the simple and simply connected algebraic groups in the positive characteristic are only a few investigated. They are well-known for some simple modules of small dimension and for the simple algebraic groups of rank 2. The third cohomology groups of simple modules for SL2 has not studied yet. In this paper the third cohomology groups of simple modules for SL2 over algebraically closed field k of characteristic p > 3 are calculated.