1999/03/23 by J. Marion, Jean Luc Marion, Marion, J. +2
Mathematics · Physics and Astronomy · #22D25 #22E65 #46K10 #58B25 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.MP #math.OA #msc:22D25 #msc:22E65 #msc:46K10 #msc:58B25
paper · pdf · doi:10.48550/arxiv.math-ph/9903037
latex, 27 pages, uses thmdefs.sty, tcilatex.tex
arxiv created 1999/03/23 · openalex publication_date 1999/03/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of good spectral triple is initiated. We prove firstly that any regular spectral triple may be embedded in a good spectral triple, so that, in non-commutative geometry, we can restricts to deal only with good spectral triples. Given a good spectral triple K=(A,H,D), we prove that A is naturally endowed with a topology, called the K-topology, making it into an unital Frechet pre C*-algebra, and that the group Inv(A) of its invertible elements has a canonical structure of Frechet Lie group of Campbell-Baker-Hausdorff type open in its Lie algebra A; moreover, for any n>0 one has that Kn=(Mn(A), H⊗ Cn,D⊗ In) is still a good spectral triple. One deduces three important consequences.