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International Journal of Mathematics and Mathematical Sciences
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Formal Lagrangian Operad

Formal Lagrangian operad
Authors: Alberto S. Cattaneo; Benoit Richard Umbert Dherin; Giovanni Felder;

Formal Lagrangian Operad

Abstract

Given a symplectic manifold M, we may define an operad structure on the the spaces Ok of the Lagrangian submanifolds of via symplectic reduction. If M is also a symplectic groupoid, then its multiplication space is an associative product in this operad. Following this idea, we provide a deformation theory for symplectic groupoids analog to the deformation theory of algebras. It turns out that the semiclassical part of Kontsevich′s deformation of C∞(ℝd) is a deformation of the trivial symplectic groupoid structure of T∗ℝd.

Country
Switzerland
Related Organizations
Keywords

Deformation quantization, star products, deformation theory of algebras, FOS: Physical sciences, Symplectic manifolds (general theory), Mathematical Physics (math-ph), 10123 Institute of Mathematics, 510 Mathematics, operad structure, Mathematics - Symplectic Geometry, 2601 Mathematics (miscellaneous), QA1-939, FOS: Mathematics, Symplectic Geometry (math.SG), symplectic reduction, symplectic groupoid, Mathematics, Mathematical Physics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
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gold