2002/04/05 by Debashish Goswami, Goswami, Debashish
Mathematics · Physics and Astronomy · #58B34 #81R50 #FOS: Mathematics #FOS: Physical sciences #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.KT #math.MP #math.QA #msc:58B34 #msc:81R50
paper · pdf · doi:10.48550/arxiv.math-ph/0204010
arxiv created 2002/04/05 · arxiv updated 2009/11/30
We study the "quantized calculus" corresponding to the algebraic ideas related to "twisted cyclic cohomology" introduced in [KMT]. With very similar definitions and techniques as those used in [jlo], we define and study "twisted entire cyclic cohomology" and the "twisted Chern character" associated with an appropriate operator-theoretic data called "twisted spectral data", which consists of a spectral triple in the conventional sense of noncommutative geometry ([Con]) and an additional positive operator having specified properties. Furthermore, it is shown that given a spectral triple (in the conventional sense) which is equivariant under the action of a compact matrix pseudogroup, it is possible to obtain a canonical twisted spectral data and hence the corresponding (twisted) Chern character, which will be invariant under the action of the pseudogroup, in contrast to the fact that the Chern character coming from the conventional noncommutative geometry need not be invariant under the above action.