Hochschild cohomology of U(sl2)

Abstract

Let k be an algebraically closed field of characteristic p > 2. We determine the Hochschild cohomology of $U(\mathtt{s}{\mathfrak{l}}_2(k))$ and the invariants of $\mathtt{s}{\mathfrak{l}}_2(k)$ and $S{L}_2(k)$ in the adjoint action on the divided power algebra $D(\mathtt{s}{\mathfrak{l}}_2(k))$.

Keywords:

• Divided powers
• Hochschild cohomology
• Lie algebras
• universal enveloping algebras

2010 Mathematics Subject Classification:

• 17B56
• 16E40