2017/08/31 by Prince K. Osei, Prince K Osei, Bernd J. Schroers +1
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Topics in Algebra #Bilinear interpolation #Black Holes and Theoretical Physics #Chern–Simons theory #Complexification #Gauge theory #Mathematical physics #Mathematics #Matrix (chemical analysis) #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1361-6382/aaaa5e
published as Class. Quantum Grav.35 (2018) 075006 · 20 pages, minor corrections and comments added in v2
openalex created_date 2017/08/31 · openalex publication_date 2018/01/24 · arxiv created 2018/04/03 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/05
Abstract We study the conditions for classical r -matrices to be compatible with the generalised Chern–Simons action for 3d gravity. Compatibility means solving the classical Yang–Baxter equations with a prescribed symmetric part for each of the real Lie algebras and bilinear pairings arising in the generalised Chern–Simons action. We give a new construction of r -matrices via a generalised complexification and derive a non-linear set of matrix equations determining the most general compatible r -matrix. We exhibit new families of solutions and show that they contain some known r -matrices for special parameter values.