2003/06/02 by Pascual Jara, P. Jara, D. Llena +1 · 1 citation
Mathematics · Physics and Astronomy · #Adjoint representation #Advanced Differential Geometry Research #Advanced Topics in Algebra #Bracket #Fundamental vector field #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Lie algebra #Lie bracket of vector fields #Lie group #Noncommutative geometry #Vector field #math.RA #msc:16W30
paper · pdf · doi:10.1023/a:1025966331750
Latex, 19 pages
arxiv created 2003/06/02 · openalex publication_date 2003/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The aim of this paper is to avoid some difficulties, related with the Lie bracket, in the definition of vector fields in a non commutative setting, as they were defined by Woronowicz, Schmudgen--Schuler and Aschieri--Schupp. We extend the definition of vector fields to consider them as derivations of the algebra, through Cartan pairs introduced by Borowiec. Then, using translations, we introduce the invariant vector fields. Finally, the definition of Lie bracket realized by Dubois--Violette, considering elements in the center of the algebra, is also extended to these invariant vector fields.