We call a Lie algebra 𝔤 di-semisimple if it can be written as a vector space sum 𝔤 = 𝔰1 + 𝔰2, where 𝔰1 and 𝔰2 are semisimple subalgebras of 𝔤 and we say that 𝔤 is strongly di-semisimple if g can be written as a direct vector space sum of semisimple subalgebras. We will show that complex strongly di-semisimple Lie algebras have to be semisimple themselves. We will then use this result to show that if a pair of complex Lie algebras (𝔤,𝔫) with 𝔤 semisimple admits a so called post-Lie algebra structure, then 𝔫 must be isomorphic to 𝔤.
This is joint work with Dietrich Burde and Mina Monadjem.
This video is part of the European Non-Associative Algebra Seminar series.
