%0 Journal Article
%T Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions
%A Carolina Neira Jim¨¦nez
%A Marie Fran£¿oise Ouedraogo
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2012
%I National Academy of Science of Ukraine
%X 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.
%K pseudodifferential operators
%K odd-class
%K trace
%K determinant
%K logarithm
%K regular Lie group
%U http://dx.doi.org/10.3842/SIGMA.2012.023