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arXiv · 2112.13631

All basic quantizations of $D=3$, $N=1$ Lorentz supersymmetry

V. N. Tolstoy
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Abstract

By the supersymmetrization of a simple algebraic technique proposed in \cite{LuTo2017} 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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V. N. Tolstoy. 2021-12-27. All basic quantizations of $D=3$, $N=1$ Lorentz supersymmetry. https://arxiv.org/abs/2112.13631

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