2011/10/05 by Marco A. Farinati, Farinati, Marco A., A. Patricia Jancsa +1
Mathematics · #17B62 (Primary) #81R50 17B40 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1110.1072
openalex publication_date 2011/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
From a Lie algebra \mathfrakg satisfying Z(\mathfrakg)=0 and Λ2(\mathfrakg)^\mathfrakg=0 (in particular, for \g semisimple) we describe explicitly all Lie bialgebra structures on extensions of the form \mathfrakL =\mathfrakg× \mathbbK in terms of Lie bialgebra structures on \mathfrakg (not necessarily factorizable nor quasi-triangular) and its biderivations, for any field \mathbbK with char \mathbbK=0. If moreover, [\mathfrakg,\mathfrakg]=\mathfrakg, then we describe also all Lie bialgebra structures on extensions \mathfrakL =\mathfrakg× \mathbbKn. In interesting cases we characterize the Lie algebra of biderivations.