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Good spectral triples, associated Lie groups of Campbell-Baker-Hausdorff type and unimodularity | | J. Marion
; K. Valavane
; | | Date: |
23 Mar 1999 | | Subject: | Mathematical Physics; Operator Algebras MSC-class: 22E65, 58B25, 46K10, 22D25 | math-ph math.MP math.OA | | Abstract: | 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 K_n=(M_n(A), Hotimes C^n,Dotimes I_n) is still a good spectral triple. One deduces three important consequences. | | Source: | arXiv, math-ph/9903037 | | Services: | Forum | Review | PDF | Favorites | |
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