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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

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 o...

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Main Authors: Neira Jimenez, Carolina, Ouedraogo, Marie-Françoise
Format: Article
Language:English
Published: Інститут математики НАН України 2012
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/148415
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spelling irk-123456789-1484152019-02-19T01:30:33Z Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions Neira Jimenez, Carolina Ouedraogo, Marie-Françoise 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. 2012 Article Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions / Carolina Neira Jimenez, Marie-Françoise Ouedraogo // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 33 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58J40; 47C05 DOI: http://dx.doi.org/10.3842/SIGMA.2012.023 http://dspace.nbuv.gov.ua/handle/123456789/148415 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description 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.
format Article
author Neira Jimenez, Carolina
Ouedraogo, Marie-Françoise
spellingShingle Neira Jimenez, Carolina
Ouedraogo, Marie-Françoise
Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Neira Jimenez, Carolina
Ouedraogo, Marie-Françoise
author_sort Neira Jimenez, Carolina
title Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions
title_short Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions
title_full Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions
title_fullStr Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions
title_full_unstemmed Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions
title_sort classification of traces and associated determinants on odd-class operators in odd dimensions
publisher Інститут математики НАН України
publishDate 2012
url http://dspace.nbuv.gov.ua/handle/123456789/148415
citation_txt Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions / Carolina Neira Jimenez, Marie-Françoise Ouedraogo // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 33 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT neirajimenezcarolina classificationoftracesandassociateddeterminantsonoddclassoperatorsinodddimensions
AT ouedraogomariefrancoise classificationoftracesandassociateddeterminantsonoddclassoperatorsinodddimensions
first_indexed 2023-05-20T17:30:39Z
last_indexed 2023-05-20T17:30:39Z
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