By François Rouvière

ISBN-10: 3319097725

ISBN-13: 9783319097725

accumulating and updating effects scattered in magazine articles over thirty years, this self-contained monograph offers a finished creation to the topic. Its aim is to: - encourage and clarify the tactic for normal Lie teams, decreasing the facts of deep leads to invariant research to the verification of 2 formal Lie bracket identities with regards to the Campbell-Hausdorff formulation (the "Kashiwara-Vergne conjecture"); - provide a close facts of the conjecture for quadratic and solvable Lie algebras, that is fairly ordinary; - expand the strategy to symmetric areas; right here an obstruction seems, embodied in one notable item known as an "e-function"; - clarify the position of this functionality in invariant research on symmetric areas, its relation to invariant differential operators, suggest price operators and round services; - provide an specific e-function for rank one areas (the hyperbolic spaces); - build an e-function for normal symmetric areas, within the spirit of Kashiwara and Vergne's unique paintings for Lie teams. The booklet contains a whole rewriting of numerous articles by way of the writer, up-to-date and stronger following Alekseev, Meinrenken and Torossian's fresh proofs of the conjecture. The chapters are mostly autonomous of one another. a few open difficulties are advised to inspire destiny examine. it truly is aimed toward graduate scholars and researchers with a easy wisdom of Lie theory.

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Symmetric Spaces and the Kashiwara-Vergne Method (Lecture Notes in Mathematics) by François Rouvière


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