1997/03/03 by Shahn Majid, S. Majid, Majid, S. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.q-alg/9703004
32 pages LATEX, no figures
arxiv created 1997/03/03 · openalex publication_date 1997/03/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce braided Lie bialgebras as the infinitesimal version of braided groups. They are Lie algebras and Lie coalgebras with the coboundary of the Lie cobracket an infinitesimal braiding. We provide theorems of transmutation, Lie biproduct, bosonisation and double-bosonisation relating braided Lie bialgebras to usual Lie bialgebras. Among the results, the kernel of any split projection of Lie bialgebras is a braided-Lie bialgebra. The Kirillov-Kostant Lie cobracket provides a natural braided-Lie bialgebra on any complex simple Lie algebra g, as the transmutation of the Drinfeld-Sklyanin Lie cobracket. Other nontrivial braided-Lie bialgebras are associated to the inductive construction of simple Lie bialgebras along the C and exceptional series.