2013/02/02 by Gabriel, Olivier, Grensing, Martin
#46L87 (Primary) #58B34 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1302.0426
In this article, we give a general construction of spectral triples from certain Lie group actions on unital C*-algebras. If the group G is compact and the action is ergodic, we actually obtain a real and finitely summable spectral triple which satisfies the first order condition of Connes' axioms. This provides a link between the "algebraic" existence of ergodic action and the "analytic" finite summability property of the unbounded selfadjoint operator. More generally, for compact G we carefully establish that our (symmetric) unbounded operator is essentially selfadjoint. Our results are illustrated by a host of examples - including noncommutative tori and quantum Heisenberg manifolds.