Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions

Symmetry Integrability and Geometry-Methods and Applications

article

Carolina Neira Jiménez¹  Marie Françoise Ouedraogo² 

[1] Fakultät für Mathematik, Universität Regensburg;Université de Ouagadougou

关键词: pseudodif ferential operators;    odd-class;    trace;    determinant;    logarithm;    regular Lie group;   

DOI  :  10.3842/SIGMA.2012.023

来源: National Academy of Science of Ukraine

【 摘 要 】

To supplement the already known classification of traces on classical pseudodifferential operators, we present a classification of traces on the algebras of odd-class pseudodifferential operators of non-positive order acting on smooth functions on a closed odd-dimensional manifold. By means of the one to one correspondence between continuous traces on Lie algebras and determinants on the associated regular Lie groups, we give a classification of determinants on the group associated to the algebra of odd-class pseudodifferential operators with fixed non-positive order. At the end we discuss two possible ways to extend the definition of a determinant outside a neighborhood of the identity on the Lie group associated to the algebra of odd-class pseudodifferential operators of order zero.

【 授权许可】

Unknown