2008/12/17 by Charles A. S. Young, C. A. S. Young, Robin Zegers +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Black Holes and Theoretical Physics #Cohomology #Contractible space #Geometry #Hopf algebra #Invertible matrix #Lie algebra #Mathematics #Noncommutative and Quantum Gravity Theories #Pure mathematics #Twist #Type (biology) #Universal enveloping algebra #hep-th #math.QA #msc:17B37 #msc:17B56 #msc:81R50
paper · pdf · doi:10.1007/s00220-010-1086-8
published as Commun.Math.Phys.298:585-611,2010 · 32 pages
arxiv created 2008/12/17 · openalex publication_date 2010/07/11 · arxiv updated 2014/11/18 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/23
One way to obtain Quantized Universal Enveloping Algebras (QUEAs) of non-semisimple Lie algebras is by contracting QUEAs of semisimple Lie algebras. We prove that every contracted QUEA in a certain class is a cochain twist of the corresponding undeformed universal envelope. Consequently, these contracted QUEAs possess a triangular quasi-Hopf algebra structure. As examples, we consider kappa-Poincare in 3 and 4 spacetime dimensions.