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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| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148415 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148415 |
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dspace |
| 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 |
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2023-05-20T17:30:39Z |
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1796153455300050944 |