%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