The local index formula for quantum SU(2)
Ludwik Dabrowski
TL;DR
This paper discusses the application of Connes--Moscovici's local index formula to the noncommutative geometry of quantum SU(2), detailing the cosphere bundle, dimension spectrum, and cyclic cocycles involved.
Contribution
It provides a detailed analysis of the local index formula in the context of quantum SU(2), expanding the understanding of noncommutative geometric structures.
Findings
Explicit description of the cosphere bundle for quantum SU(2)
Identification of the dimension spectrum in this setting
Construction of local cyclic cocycles for the index formula
Abstract
The local index formula of Connes--Moscovici for the isospectral noncommutative geometry recently constructed on quantum SU(2) is discussed. The cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula, are presented.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Noncommutative and Quantum Gravity Theories · Algebraic structures and combinatorial models