2015/04/19 by Yi-Nan Wang, Wang, Yi-Nan · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebra over a field #Algebraic number #Black Holes and Theoretical Physics #Calculus (dental) #Computer science #Cosmology and Gravitation Theories #Differential (mechanical device) #Differential calculus #Differential form #Dimension (graph theory) #Extension (predicate logic) #FOS: Physical sciences #Field (mathematics) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Physics #Pure mathematics #Tensor calculus #Tensor field #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1504.04780
30 pages
openalex publication_date 2015/04/19 · arxiv created 2015/06/18 · arxiv updated 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We develop the generalized Cartan Calculus for the groups G=SL(2,ℝ)×ℝ+, SL(5,ℝ) and SO(5,5). They are the underlying algebraic structures of d=9,7,6 exceptional field theory, respectively. These algebraic identities are needed for the "tensor hierarchy" structure in exceptional field theory. The validity of Poincaré lemmas in this new differential geometry is also discussed. Finally we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.