2007/06/09 by Barben-Jean Coffi-Nketsia, Coffi-Nketsia, Barben-Jean, Labib Haddad +1
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.0706.1312
A moderately detailed english summary of the paper can be found on pages 9 to 15, in "Produit d'entrelacement et action triangulaire d'algèbres de Lie", arXiv:math.RT/0704.3840v1
arxiv created 2007/06/09 · openalex publication_date 2007/06/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Full details are given for the definition and construction of the wreath product of two arbitrary Lie algebras, in the hope that it can lead to the definition of a suitable Lie group to be the wreath product of two given Lie groups. In the process, quite a few new notions are needed, and introduced. Such are, for example : Formal series with variables in a vector space and coefficients in some other vector space. Derivation of a formal series relative to another formal series. The Lie algebra of a vector space. Formal actions of Lie algebras over vector spaces. The basic formal action of a Lie algebra over itself (as a formal version of the analytic aspect of the infinitesimal operation law of a Lie groupuscule). More generally, the wreath product of two Lie algebras is defined, relative to a formal action of the second onto an arbitrary vector space. Main features are : A description of the triangular actions of wreath products over product vector spaces, and a Kaloujnine-Krasner type theorem : In essence, it says that all Lie extensions of a given Lie algebra by another Lie algebra are, indeed, subalgebras of their wreath product.