(based on joint work with Marta Mazzocco)
We introduce the generalization of groupoids of upper-triangular matrices by Bondal to the case where the matrix A is composed from the $m\times m$-blocks. We find the corresponding algebroid structure and the Poisson brackets for entries of A. These brackets are independent on m and coincide with those in the case of Sp(2n) algebra investigated by Molev, Ragoucy and Sorba. The affinnization of these brackets is the twisted Yangian algebra; we find the action of the (affine) braid group and all the central elements of this algebra.