PIRASHVILI'S CONJECTURE ON THE LEIBNIZ HOMOLOGY FOR LIE ALGEBRAS

Dietrich Burde , Friedrich Wagemann (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

We prove a conjecture of Pirashvili, which says that a non-trivial finite-dimensional complex Lie algebra g is semisimple if and only if its Leibniz (co)homology with trivial coefficients vanishes. We also prove several results on the Lie and Leibniz cohomology of perfect and complete Lie algebras.

Domaines: Topologie algébrique [math.AT]

Dietrich Burde, Friedrich Wagemann. PIRASHVILI'S CONJECTURE ON THE LEIBNIZ HOMOLOGY FOR LIE ALGEBRAS. 2019. ⟨hal-02266972⟩