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Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions
Інший ID:
2010 Mathematics Subject Classification: 58J40; 47C05
DOI: http://dx.doi.org/10.3842/SIGMA.2012.023
DOI: http://dx.doi.org/10.3842/SIGMA.2012.023
Посилання:
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.
Підтримка:
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.
Дата:
2012
Переглядів:
628
Завантажень:
194
Анотація:
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.
