Contents
Chapter 1. Introduction 1
Chapter 2. A class of biequivariant Poisson groupoids 5
2.1. Preliminaries 5
2.2. Trivial Lie groupoids in CJJ 8
Chapter 3. Duality 17
3.1. Duality of Poisson groupoids 17
3.2. The dual of a dynamical Poisson groupoid 19
Chapter 4. An explicit case study of duality 26
Chapter 5. Coboundary dynamical Poisson groupoids - the constant r-
matrix case 34
5.1. The dual Poisson groupoid 34
5.2. Construction of the associated symplectic double groupoid 42
Appendix 65
A.l. Proof of Proposition 2.2.3 65
A.2. Proof of Theorem 2.2.5 (b) 66
A.3. Proof of Proposition 3.2.1 67
A.4. Proof of the coisotropy in Theorem 5.1.4 69
Bibliography 71
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