2019/06/24 by Dietrich Burde, Burde, Dietrich, Vsevolod Gubarev +1
Mathematics · #17B20 #17D25 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:17B20 #msc:17D25
paper · pdf · doi:10.48550/arxiv.1906.09854
arxiv created 2019/06/24 · arxiv updated 2019/06/25
We introduce post-associative algebra structures and study their relationship to post-Lie algebra structures, Rota--Baxter operators and decompositions of associative algebras and Lie algebras. We show several results on the existence of such structures. In particular we prove that there exists no post-Lie algebra structure on a pair (\mathfrakg,\mathfrakn), where \mathfrakn is a simple Lie algebra and \mathfrakg is a reductive Lie algebra, which is not isomorphic to \mathfrakn. We also show that there is no post-associative algebra structure on a pair (A,B) arising from a Rota--Baxter operator of B, where A is a semisimple associative algebra and B is not semisimple. The proofs use results on Rota--Baxter operators and decompositions of algebras.