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...

Повний опис

Збережено в:
Бібліографічні деталі
Дата:2012
Автори: Neira Jimenez, Carolina, Ouedraogo, Marie-Françoise
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2012
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
Опис
Резюме: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.