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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148415 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862737839909765120 |
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| author | Neira Jimenez, Carolina Ouedraogo, Marie-Françoise |
| author_facet | Neira Jimenez, Carolina Ouedraogo, Marie-Françoise |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T20:01:28Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148415 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:01:28Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Neira Jimenez, Carolina Ouedraogo, Marie-Françoise 2019-02-18T12:04:10Z 2019-02-18T12:04:10Z 2012 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 https://nasplib.isofts.kiev.ua/handle/123456789/148415 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. We are very grateful to Professor Sylvie Paycha for her advice and encouragement along an important part of our careers. We express our gratitude to the Max Planck Institute for
 Mathematics in Bonn and the University of Regensburg where part of this work was done.
 We would also like to thank the anonymous referees for providing constructive comments on the manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions Article published earlier |
| spellingShingle | Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions Neira Jimenez, Carolina Ouedraogo, Marie-Françoise |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148415 |
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