Good spectral triples, associated Lie groups of Campbell-Baker-Hausdorff type and unimodularity

Details Good spectral triples, associated Lie groups of Campbell-Baker-Hausdorff type and unimodularity Good spectral triples, associated Lie groups of Campbell-Baker-Hausdorff type and unimodularity

1999-03-23

arxiv.org/abs/math-ph/9903037v1

Physics

Mathematical Physics

latex, 27 pages, uses thmdefs.sty, tcilatex.tex

Scientific paper

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), H\otimes C^n,D\otimes I_n) is still a good spectral triple. One deduces three important consequences.

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