Lie Bialgebroid of Pseudo-differential Operators

Author:

Eslami Rad Anahita

Abstract

AbstractWe associate a Lie bialgebroid structure to the algebra of formal Pseudo-differential operators, as the classical limit of a quantum groupoid. As a consequence, the non-commutative Kadomtsev–Petviashvili hierarchy is naturally obtained by an algebraic procedure.

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Reference24 articles.

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3. Calaque, D., Dolgushev, V., Halbout, G.: Formality Theorems for Hochschild chains in the Lie Algebroid setting. Journal fur die reine und angewandte Mathematik (Crelles Journal) 612, 81–127 (2007)

4. Cannas da Silva, A., Weinstein, A.: Geometric Models for Noncommutative Algebras. Berkeley Mathematics Lecture Notes 10, American Mathematical Society, Providence, Rhode Island (1999)

5. Chari, V., Pressley, A.: A Guide to Quantum Groups. Cambridge University Press, Cambridge (1994)

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