Using a suitable extension of Drinfel’d double we derive formulas for the Poisson–Lie T-plurality transformation with spectators, i.e., for σ-models whose group of generalized isometries does not act transitively on the target manifold. These formulas are further applied to transformations of the gluing matrices that define the boundary conditions of the σ-models.
Defining the real Lie superalgebra as real Z2-graded vector space we classify real Manin supertriples and Drinfel’d superdoubles of superdimensions (2,2), (4,2), and (2,4). The Drinfel’d doubles of the superdimension (2,2) are then used for construction of the simplest σ-models related by Poisson–Lie T-plurality.
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