2021/12/27 by Tolstoy, V. N.
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2112.13631
By the supersymmetrization of a simple algebraic technique proposed in \citeLuTo2017 we obtain the complete classification of all basic (nonisomorphic) quantum deformations for the orthosymplectic Lie superalgebra \mathfrakosp(1|2;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 \mathfrakosp(1|2;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.