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

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

2011-11-29

arxiv.org/abs/1111.6750v2

SIGMA 8 (2012), 023, 25 pages

Mathematics

Operator Algebras

Scientific paper

10.3842/SIGMA.2012.023

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.

Affiliated with

Also associated with

No associations

Rating

Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-15233