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Quantum Deformation of the Poincare Supergroup and $κ$-deformed Superspace

P. Kosi{ń}ski·J. Lukierski·P. Ma{ś}lanka·J. Sobczyk
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Abstract

The classical $r$-matrix for $N=1$ superPoincar{é} algebra, given by Lukierski, Nowicki and Sobczyk is used to describe the graded Poisson structure on the $N=1$ Poincar{é} supergroup. The standard correspondence principle between the even (odd) Poisson brackets and (anti)commutators leads to the consistent quantum deformation of the superPoincar{é} group with the deformation parameter $q$ described by fundamental mass parameter $κ\quad (κ^{-1}=\ln{q})$. The $κ$-deformation of $N=1$ superspace as dual to the $κ$-deformed supersymmetry algebra is discussed.

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P. Kosi{ń}ski, J. Lukierski, P. Ma{ś}lanka, J. Sobczyk. 1994-05-11. Quantum Deformation of the Poincare Supergroup and $κ$-deformed Superspace. https://doi.org/10.1088/0305-4470%2F27%2F20%2F019

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