Burde Dietrich, Dekimpe Karel, Monadjem Mina
Fakultät für Mathematik, Universität Wien, Wien, Austria.
Katholieke Universiteit Leuven Kulak, Kortrijk, Belgium.
Commun Algebra. 2024 May 15;52(10):4255-4267. doi: 10.1080/00927872.2024.2344638. eCollection 2024.
We study the existence of post-Lie algebra structures on pairs of Lie algebras , where one of the algebras is perfect non-semisimple, and the other one is abelian, nilpotent non-abelian, solvable non-nilpotent, simple, semisimple non-simple, reductive non-semisimple or complete non-perfect. We prove several nonexistence results, but also provide examples in some cases for the existence of a post-Lie algebra structure. Among other results we show that there is no post-Lie algebra structure on , where is perfect non-semisimple, and is . We also show that there is no post-Lie algebra structure on , where is perfect and is reductive with a 1-dimensional center.
我们研究李代数对 上后李代数结构的存在性，其中一个代数是完备非半单的，另一个是阿贝尔的、幂零非阿贝尔的、可解非幂零的、单的、半单非单的、约化非半单的或完备非完备的。我们证明了几个不存在性结果，但也在某些情况下给出了后李代数结构存在的例子。在其他结果中，我们表明在 上不存在后李代数结构，其中 是完备非半单的，且 是 。我们还表明在 上不存在后李代数结构，其中 是完备的且 是具有一维中心的约化的。
