2014/04/10 by Partha Sarathi Chakraborty, Satyajit Guin, Chakraborty, Partha Sarathi +1
Mathematics · #16E45 #46L87 #58B34 #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:16E45 #msc:46L87 #msc:58B34
paper · pdf · doi:10.48550/arxiv.1404.2708
arxiv created 2014/04/10 · arxiv updated 2014/04/11
Given a spectral triple (A,H,D) Connes associated a canonical differential graded algebra ΩD^\bullet(A). However, so far this has been computed for very few special cases. We identify suitable hypotheses on a spectral triple that helps one to compute the associated Connes' calculus for its quantum double suspension. This allows one to compute ΩD^\bullet for spectral triples obtained by iterated quatum double suspension of the spectral triple associated with a first order differential operator on a compact smooth manifold. This gives the first systematic computation of Connes' calculus for a large family of spectral triples.