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Abstract
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We obtain inequivalent classical r-matrices of the 𝑜𝑠𝑝(1|2) Lie superalgebra as real solutions of the graded (modified)
classical Yang-Baxter equation, in such a way that the corresponding automorphism transformation is
employed. Then, Yang-Baxter deformations of the Wess-Zumino-Witten model based on the OSP(1|2) Lie supergroup
are specified by super skew-symmetric classical r-matrices. In this regard, the effect coming from the
deformation is reflected as the coefficient of both metric and 𝐵-field. Furthermore, it is shown that all resulting
classical r-matrices are non-Abelian and also non-unimodular, which leads us to graded generalized supergravity
equations. We show that the background of undeformed model is a solution of the graded generalized supergravity
equations when supplemented by an appropriate supervector field obtaining from the linear combination of
the Killing supervectors corresponding to the background, while the deformed models do not satisfy these equations.
This is consistent with our expectations, since the deformed models under consideration do not describe
a Green-Schwarz superstring. However, the deformed backgrounds are interesting, in particular in the OSP(1|2)
case they are rare, much hard technical work was needed to obtain them.
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