WEIGHTED TRACES ON ALGEBRAS OF PSEUDO-DIFFERENTIAL OPERATORS AND GEOMETRY ON LOOP GROUPS

DOI10.1142/S021902570200095XzbMath1134.58303arXivmath/0001117OpenAlexW2963834873WikidataQ115245789 ScholiaQ115245789MaRDI QIDQ4818910

Catherine Ducourtioux, Jean-Pierre Magnot, Sylvie Paycha, Alexander Cardona

Publication date: 24 September 2004

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0001117

zbMATH Keywords

loop groupspseudo-differential operatorsRegularized traces

Mathematics Subject Classification ID

Loop groups and related constructions, group-theoretic treatment (22E67) Pseudodifferential and Fourier integral operators on manifolds (58J40) Noncommutative global analysis, noncommutative residues (58J42) Pseudodifferential operators (47G30) Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) (47L80) Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc. (35S35)

Related Items (18)

On \(\mathrm{Diff}(M)\)-pseudo-differential operators and the geometry of non linear Grassmannians ⋮ (Second) Quantised resolvents and regularised traces ⋮ On diffeological principal bundles of non-formal pseudo-differential operators over formal ones ⋮ Renormalized traces and cocycles on the algebra of \(S^{1}\)-pseudo-differential operators ⋮ From tracial anomalies to anomalies in quantum field theory ⋮ The local and global parts of the basic zeta coefficient for operators on manifolds with boundary ⋮ The multiplicative anomaly for determinants revisited; locality ⋮ On the Logarithm Component in Trace Defect Formulas ⋮ The Schwinger cocycle on algebras with unbounded operators ⋮ UNIQUENESS OF TRACES ON LOG-POLYHOMOGENEOUS PSEUDODIFFERENTIAL OPERATORS ⋮ Anomalies and Schwinger terms in NCG field theory models ⋮ Generalized Yang–Mills actions from Dirac operator determinants ⋮ Symmetrized trace and symmetrized determinant of odd class pseudo-differential operators ⋮ Chern forms on mapping spaces ⋮ On the Kadomtsev-Petviashvili hierarchy in an extended class of formal pseudo-differential operators ⋮ On the geometry of $Diff(S^1)$-pseudodifferential operators based on renormalized traces. ⋮ The Dixmier Trace and the Noncommutative Residue for Multipliers on Compact Manifolds ⋮ Curvature on determinant bundles and first Chern forms

Cites Work

• A central extension of the algebra of pseudodifferential symbols
• The analysis of elliptic families. I: Metrics and connections on determinant bundles
• Regularisable and minimal orbits for group actions in infinite dimensions
• On the noncommutative residue for pseudodifferential operators with log-polyhomogeneous symbols
• Differential geometry of Grassmannian embeddings of based loop groups
• Lie algebras of differential operators, their central extensions, and W- algebras
• Symplectic geometry of the loop space of a Riemannian manifold
• Schwinger terms and cohomology of pseudodifferential operators
• Logarithmic Sobolev inequalities for pinned loop groups
• The homotopy type of the unitary group of Hilbert space
• RENORMALIZED LAPLACIANS ON A CLASS OF HILBERT MANIFOLDS AND A BOCHNER–WEITZENBÖCK TYPE FORMULA FOR CURRENT GROUPS
• RENORMALIZED TRACES AS A LOOKING GLASS INTO INFINITE-DIMENSIONAL GEOMETRY
• The Energy Flow on the Loop Space of a Compact Lie Group

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