2002/01/31 by Rainer Matthes, R. Matthes, O. Richter +2
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Differential (mechanical device) #Differential operator #Dirac (video compression format) #Dirac operator #Foliation (geology) #Geometry #Kronecker delta #Mathematical analysis #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Operator (biology) #Order (exchange) #Physics #Pure mathematics #Signature (topology) #Spectral Theory in Mathematical Physics #Spectral triple #TRACE (psycholinguistics) #Torus #math-ph #math.MP #msc:16W25 #msc:81V15
paper · pdf · doi:10.1016/s0393-0440(02)00136-5
27 pages
arxiv created 2002/01/31 · openalex publication_date 2003/02/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Following ideas of Connes and Moscovici, we describe two spectral triples related to the Kronecker foliation, whose generalized Dirac operators are related to first and second order signature operators. We also consider the corresponding differential calculi ΩD, which are drastically different in the two cases. As a side-remark, we give a description of a known calculus on the two-dimensional noncommutative torus in terms of generators and relations.