Canonical Basis for Quantum {mathfrak{osp}(1|2)}

We introduce a modified quantum enveloping algebra as well as a (modified) covering quantum algebra for the ortho-symplectic Lie superalgebra ${mathfrak{osp}(1|2)}$ . Then we formulate and compute the corresponding canonical bases, and relate them to the counterpart for ${mathfrak{sl}(2)}$ . This provides a first example of canonical basis for quantum superalgebras.