Quantum torus algebras and B(C) type Toda systems

In this paper, we construct a new even constrained B© type Toda hierarchy and derive its B© type Block type additional symmetry. Also we generalize the B© type Toda hierarchy to the $N$-component B© type Toda hierarchy which is proved to have symmetries of a coupled ${⨂}^{N}Q{T}_{+}$ algebra ( $N$-folds direct product of the positive half of the quantum torus algebra $QT$).