Geodesic
A~symplectic groupoid of triangular bilinear forms and the braid group
Izvestiya. Mathematics , Tome 68 (2004) no. 4, pp. 659-708

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We construct a symplectic groupoid of triangular bilinear forms and establish a relation with the flag variety. We also study the induced Poisson structure and the centre of the corresponding algebroid. 
@article{IM2_2004_68_4_a1,
     author = {A. I. Bondal},
     title = {A~symplectic groupoid of triangular bilinear forms and the braid group},
     journal = {Izvestiya. Mathematics },
     pages = {659--708},
     publisher = {mathdoc},
     volume = {68},
     number = {4},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2004_68_4_a1/}
}
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A. I. Bondal. A~symplectic groupoid of triangular bilinear forms and the braid group. Izvestiya. Mathematics , Tome 68 (2004) no. 4, pp. 659-708. http://geodesic.mathdoc.fr/item/IM2_2004_68_4_a1/