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In this paper, we construct a series of additional flows of the CKP hierarchyand the multi-component CKP hierarchy and these flows constitute a N-foldsdirect product of the positive half of the quantum Torus symmetry. Comparing tothe $W_{\infty}$ infinite dimensional Lie symmetry, this quantum Torus symmetryhas a nice algebraic structure with double indices.

Quantum Torus symmetries of the CKP and multi-component CKP hierarchies