Abstract
By the supersymmetrization of a simple algebraic technique proposed in Lukierski and Tolstoy (Eur Phys J C 77:226, 2017) we obtain the complete classification of all basic (nonisomorphic) quantum deformations for the orthosymplectic Lie superalgebra mathfrak {osp}(1|2;{mathbb {C}}) and its pseudoreal and real forms in terms of the classical r-matrices. In particular, we prove that pseudoreal compact form has only one quantum deformation (standart q-analog), and the D=3, N=1 Lorentz supersymmetry, which is the non-compact real form of mathfrak {osp}(1|2;{mathbb {C}}), has four different Hopf-algebraic quantum deformations: two standard q-analogs, and two (Jordanian and super-Jordanian) twist deformations. All basic Hopf-algebraic quantum deformations are presented in the explicit form.
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